From arndt at jjj.de  Sun Feb  1 10:22:45 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Sun, 1 Feb 2015 10:22:45 +0100
Subject: [seqfan] polyominoes on square lattice by symmetry
Message-ID: <20150201092245.GA5191@jjj.de>

About
  P. Leroux, E. Rassart, A. Robitaille,
  <a href="http://dx.doi.org/10.1006/aama.1998.0601">
  Enumeration of Symmetry Classes of Convex Polyominoes in the Square Lattice</a>
  Advances in Applied Mathematics, vol.21, no.3, pp.343-380, (October-1998).

Could someone check which sequences given on
p.377 are missing in the OEIS?

At least 1,1,2,7,17,50,131,363,924,2380 is missing.

When entering the seqs please spell out the symmetry type
(I cannot do this, that's why am asking on the list).

Best,  jj



From info at polprimos.com  Sun Feb  1 02:11:01 2015
From: info at polprimos.com (Omar E. Pol)
Date: Sat, 31 Jan 2015 22:11:01 -0300
Subject: [seqfan] A253072.
Message-ID: <20150201011101.M80143@polprimos.com>

Dear Neil,

An observation.
In the sequences A050476 and A253072 we have that: 

a(0) = 1
a(1) = 7
a(3) = 95
a(7) = 18447

A253072(2^k-1) = A050476(2^k-1), 0<=k<=m, where m is at least 3. 

Best regards. 

Omar E. Pol


From arndt at jjj.de  Sun Feb  1 11:00:15 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Sun, 1 Feb 2015 11:00:15 +0100
Subject: [seqfan] honeycomb polyominoes
Message-ID: <20150201100015.GA5352@jjj.de>

Similar to the message before:

Dominique Gouyou-Beauchamps, Pierre Leroux,
<a href="http://dx.doi.org/10.1016/j.tcs.2005.08.025">
Enumeration of Symmetry Classes of Convex Polyominoes on the Honeycomb Lattice</a>,
Theoretical Computer Science, vol.346, no.2-3, pp.307-334, (November-2005).

p.320:
1
3
11
38
120
348
939
2412
5973
14394
34056
79602
184588
426036
980961
2256420
5189577
11939804
27485271
63308532
145903992
336418179
775996665
1790486717
4132195707
9538127076
22018993552
50835685427
117372288297
271006745255
625758286777
1444911247194
3336422923431
7704147029616
17789770663899
41078790416848
94856243572216
219035659925172
505782887350567
1167921607616731
2696891148564180
6227492958077133
14380140755028117
33205732845460311
76676631829002129
177056959135248647
408849042325490952
944089080678393018
2180032500563641911
5033997137232724122
11624197004721262104
26841881829357335687


And, at end of page:
0, 0, 1, 0, 3, 2, 12, 18, 59, 120, 318, 714, 1743, ...


Also p.322: 1, 1, 3, 6, 15, 38, 91, 222, 528, 1250, ...

Also several seqs on p.333


Best,  jj


From njasloane at gmail.com  Sun Feb  1 19:35:37 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Sun, 1 Feb 2015 13:35:37 -0500
Subject: [seqfan] Re: A253072.
In-Reply-To: <20150201011101.M80143@polprimos.com>
References: <20150201011101.M80143@polprimos.com>
Message-ID: <CAAOnSgTtnjbzYHGjrP+jWg2ZgirDjX8BObdKcFFu_fNRBMhAdA@mail.gmail.com>

Interesting comment!  Of course it might be a coincidence.  Still, I added
it to A253072.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Jan 31, 2015 at 8:11 PM, Omar E. Pol <info at polprimos.com> wrote:

> Dear Neil,
>
> An observation.
> In the sequences A050476 and A253072 we have that:
>
> a(0) = 1
> a(1) = 7
> a(3) = 95
> a(7) = 18447
>
> A253072(2^k-1) = A050476(2^k-1), 0<=k<=m, where m is at least 3.
>
> Best regards.
>
> Omar E. Pol
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From arndt at jjj.de  Mon Feb  2 19:18:21 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Mon, 2 Feb 2015 19:18:21 +0100
Subject: [seqfan] Re: polyominoes on square lattice by symmetry
In-Reply-To: <20150201092245.GA5191@jjj.de>
References: <20150201092245.GA5191@jjj.de>
Message-ID: <20150202181821.GA6579@jjj.de>

Will do all of this (incl. other message) myself,
but may well be in several weeks from now.

Best regards,  jj

* Joerg Arndt <arndt at jjj.de> [Feb 01. 2015 12:03]:
> About
>   P. Leroux, E. Rassart, A. Robitaille,
>   <a href="http://dx.doi.org/10.1006/aama.1998.0601">
>   Enumeration of Symmetry Classes of Convex Polyominoes in the Square Lattice</a>
>   Advances in Applied Mathematics, vol.21, no.3, pp.343-380, (October-1998).
> 
> Could someone check which sequences given on
> p.377 are missing in the OEIS?
> 
> At least 1,1,2,7,17,50,131,363,924,2380 is missing.
> 
> When entering the seqs please spell out the symmetry type
> (I cannot do this, that's why am asking on the list).
> 
> Best,  jj
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/


From penson at lptl.jussieu.fr  Tue Feb  3 00:24:08 2015
From: penson at lptl.jussieu.fr (Karol)
Date: Tue, 03 Feb 2015 00:24:08 +0100
Subject: [seqfan] Question on A005572 from K. A. Penson
Message-ID: <54D00718.50007@lptl.jussieu.fr>

Does anybody know how to obtain the close form of A005572(n) ?

Thanking in advance,

     Karol A. Penson


From maxale at gmail.com  Tue Feb  3 00:52:29 2015
From: maxale at gmail.com (Max Alekseyev)
Date: Mon, 2 Feb 2015 18:52:29 -0500
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
In-Reply-To: <54D00718.50007@lptl.jussieu.fr>
References: <54D00718.50007@lptl.jussieu.fr>
Message-ID: <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>

Hi Karol,

There is a formula

A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,

which expands (with substitution k -> n-2k) into:

A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
(k+1) * 4^(n-2k)

PARI/GP code:

{ A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
* 4^(n-2*k) ) }

Regards,
Max



On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
> Does anybody know how to obtain the close form of A005572(n) ?
>
> Thanking in advance,
>
>     Karol A. Penson
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/


From israel at math.ubc.ca  Tue Feb  3 02:46:31 2015
From: israel at math.ubc.ca (israel at math.ubc.ca)
Date: 02 Feb 2015 17:46:31 -0800
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
In-Reply-To: <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>
References: <54D00718.50007@lptl.jussieu.fr>
 <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>
Message-ID: <Prayer.1.3.5.1502021746310.15725@viol.math.ubc.ca>

And, according to Maple, these sums can be written as a hypergeometric 
function:

A005572(n) = 4^n*hypergeom([-n/2, (1-n)/2], [2], 1/4)

Cheers,
Robert

On Feb 2 2015, Max Alekseyev wrote:

>Hi Karol,
>
>There is a formula
>
>A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,
>
>which expands (with substitution k -> n-2k) into:
>
>A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
>(k+1) * 4^(n-2k)
>
>PARI/GP code:
>
>{ A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
>* 4^(n-2*k) ) }
>
>Regards,
>Max
>
>
>
>On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
>> Does anybody know how to obtain the close form of A005572(n) ?
>>
>> Thanking in advance,
>>
>>     Karol A. Penson
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>


From pauldhanna at juno.com  Tue Feb  3 03:15:29 2015
From: pauldhanna at juno.com (Paul D Hanna)
Date: Tue, 3 Feb 2015 02:15:29 GMT
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
Message-ID: <20150202.211529.23111.0@webmail03.dca.untd.com>

Also, 
a(n) = Sum_{k=0..n} binomial(n,k) * 2^(n-k) * binomial(2*k+2, k)/(k+1). 
 
a(n) = Sum_{k=0..n} binomial(n,k) * 2^(n-k) * A000108(k+1). 
 
This can be derived from the relation 
a(n) = [x^n] (1+4*x+x^2)^(n+1) / (n+1) 
 
which is due to 
G.f.: (1/x) * Series_Reversion( x/(1+4*x+x^2) ).  
 
However, the formula from Max seems to be more efficient. 
      Paul 
 
---------- Original Message ----------
From: Max Alekseyev <maxale at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Cc: Karol <penson at lptl.jussieu.fr>
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
Date: Mon, 2 Feb 2015 18:52:29 -0500

Hi Karol,

There is a formula

A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,

which expands (with substitution k -> n-2k) into:

A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
(k+1) * 4^(n-2k)

PARI/GP code:

{ A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
* 4^(n-2*k) ) }

Regards,
Max



On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
> Does anybody know how to obtain the close form of A005572(n) ?
>
> Thanking in advance,
>
>     Karol A. Penson
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/



From hv at crypt.org  Tue Feb  3 18:34:58 2015
From: hv at crypt.org (hv at crypt.org)
Date: Tue, 03 Feb 2015 17:34:58 +0000
Subject: [seqfan] A113917 and A113918: zero-free squaring
Message-ID: <201502031734.t13HYwP09486@crypt.org>

Back in Jan 2006, David Wilson introduced this question:

  For a number n, let f(n) be the set of numbers gotten by splitting n^2 at
  the 0 digits.  For example

  29648^2 = 879003904

  so f(29648) = { 4, 39, 879 }

  Let S be the smallest set of numbers containing 2 and fixed by f.  What is
  the largest element of S?

.. which eventually gave A113917 (largest element) and A113918 (cardinality
of the set).

I did say at the time "I don't have full confidence in the results", but
when trying to clean up my 2006 code recently, as part of a long-running
project to push all my maths code to Github, I found several bugs which
meant some of the results were wrong. Sorry about that.

I've fixed those and further improved the code, available under 'zerofree'
in <https://github.com/hvds/seq>, and will go update the sequences on
the assumption that my new code is correct. I'd still appreciate it if
someone could confirm some or all of the values though.

I estimate the cardinality for A113918(9) is between 10^10 and 10^13,
which I can't calculate with my current approach (but I have another
approach in mind that might reach it). Given the rate of growth, I think
n=10 (ie the original question) is likely to be beyond my means.

With the new code it's easy to change the calculation, and replacing
s -> s^2 with s -> 2s gives a new pair of sequences that grows slow enough
it's easy to calculate more terms; I'm not sure if they're also worth
adding to OEIS, or if there are different calculations that would also be
of interest.

Hugo
---
With calculation s -> s^2: "n: card(n) max(n)"
2: 2 2
3: 18 1849
4: 2 2
5: 3050 266423227914725931
6: 34762 3100840870711697060720215047
7: 3087549 845486430620513036335402848567278325780455810752216401
8: 2 4

With calculation s -> 2s: "n: card(n) max(n)"
2: 2 2
3: 6 16
4: 2 2
5: 20 192
6: 13 128
7: 72 32768
8: 3 4
9: 92 69632
10: 42 23552
11: 308 25722880
12: 34 425984
13: 900 717895680
14: 178 1051828224
15: 1739 217079873536
16: 4 8
17: 3349 2270641389568
18: 443 10603200512
19: 4523 156423849771008
20: 387 950175531008
21: 14364 25160124578398208
22: 1827 385584983965696
23: 18672 450589122059304960
24: 234 40722497536
25: 39426 53279734579488838656
26: 15882 127148822502119047168
27: 52664 299326717942059499520
28: 8858 43157851113903387312128
29: 128253 13526981441472537034752
30: 28346 449522648486053412864
31: 123087 371244129204723018366976
32: 5 16
33: 259207 23655711299608586448011264
34: 87797 103182870656711001112576
35: 363512 39823687474383259120435200
36: 44545 63973308447624725004288
37: 671389 313519863989706816307303809024
38: 182549 45225850656203876163438682112
39: 1336282 31933986316064959928909955072
40: 18049 6034750858947540643601186816
41: 1289210 4145806855637690163777954119680
42: 634402 143410752413726318705389116325888
43: 2679419 251570201273324198920857495653056512
44: 156629 9442738596003761319219036160
45: 3428818 288049927140258932406824739012608
46: 987498 20384387023837630566380055072075677696
47: 5876576 16579286652350303184601394767032483840
48: 13308 152556272234873601963528260943872
49: 8122478 463424116819682991065891465214793542008832
50: 3118809 63039435236897106221986787164071919616
51: 14743535 247126135557931098912701316497011638272
52: 796352 1083181655178944127338714024967634157568
53: 15921180 71286088956163866149580753955553592475648
54: 4952057 2150676694930424720837752491965232971776
55: 29170111 507477067298501219491044453334717130866688
56: 403964 1746977513106742264740052226757623808
57: 48839762 27320774362755367988623371083844092646391808
58: 11997500 6094365163190490383475585992644805477269504
59: 71116907 9188495794580645540482153719631435565136609280
60: 2675259 14463684581762047084433709884282673037312
61: 122451245 9107655699502841924691980127153411750800769679360
62: 17820844 199082515611433949561498862265902993781030912



From njasloane at gmail.com  Wed Feb  4 01:33:51 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 3 Feb 2015 19:33:51 -0500
Subject: [seqfan] Re: A113917 and A113918: zero-free squaring
In-Reply-To: <201502031734.t13HYwP09486@crypt.org>
References: <201502031734.t13HYwP09486@crypt.org>
Message-ID: <CAAOnSgRCE4f0Bj5ADpt2nQjufdYz_j_69E+vaVp_SbJm85O4SA@mail.gmail.com>

Hans, certainly those two sequences are worth adding
to the OEIS! Please do so!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Feb 3, 2015 at 12:34 PM, <hv at crypt.org> wrote:

> Back in Jan 2006, David Wilson introduced this question:
>
>   For a number n, let f(n) be the set of numbers gotten by splitting n^2 at
>   the 0 digits.  For example
>
>   29648^2 = 879003904
>
>   so f(29648) = { 4, 39, 879 }
>
>   Let S be the smallest set of numbers containing 2 and fixed by f.  What
> is
>   the largest element of S?
>
> .. which eventually gave A113917 (largest element) and A113918 (cardinality
> of the set).
>
> I did say at the time "I don't have full confidence in the results", but
> when trying to clean up my 2006 code recently, as part of a long-running
> project to push all my maths code to Github, I found several bugs which
> meant some of the results were wrong. Sorry about that.
>
> I've fixed those and further improved the code, available under 'zerofree'
> in <https://github.com/hvds/seq>, and will go update the sequences on
> the assumption that my new code is correct. I'd still appreciate it if
> someone could confirm some or all of the values though.
>
> I estimate the cardinality for A113918(9) is between 10^10 and 10^13,
> which I can't calculate with my current approach (but I have another
> approach in mind that might reach it). Given the rate of growth, I think
> n=10 (ie the original question) is likely to be beyond my means.
>
> With the new code it's easy to change the calculation, and replacing
> s -> s^2 with s -> 2s gives a new pair of sequences that grows slow enough
> it's easy to calculate more terms; I'm not sure if they're also worth
> adding to OEIS, or if there are different calculations that would also be
> of interest.
>
> Hugo
> ---
> With calculation s -> s^2: "n: card(n) max(n)"
> 2: 2 2
> 3: 18 1849
> 4: 2 2
> 5: 3050 266423227914725931
> 6: 34762 3100840870711697060720215047
> 7: 3087549 845486430620513036335402848567278325780455810752216401
> 8: 2 4
>
> With calculation s -> 2s: "n: card(n) max(n)"
> 2: 2 2
> 3: 6 16
> 4: 2 2
> 5: 20 192
> 6: 13 128
> 7: 72 32768
> 8: 3 4
> 9: 92 69632
> 10: 42 23552
> 11: 308 25722880
> 12: 34 425984
> 13: 900 717895680
> 14: 178 1051828224
> 15: 1739 217079873536
> 16: 4 8
> 17: 3349 2270641389568
> 18: 443 10603200512
> 19: 4523 156423849771008
> 20: 387 950175531008
> 21: 14364 25160124578398208
> 22: 1827 385584983965696
> 23: 18672 450589122059304960
> 24: 234 40722497536
> 25: 39426 53279734579488838656
> 26: 15882 127148822502119047168
> 27: 52664 299326717942059499520
> 28: 8858 43157851113903387312128
> 29: 128253 13526981441472537034752
> 30: 28346 449522648486053412864
> 31: 123087 371244129204723018366976
> 32: 5 16
> 33: 259207 23655711299608586448011264
> 34: 87797 103182870656711001112576
> 35: 363512 39823687474383259120435200
> 36: 44545 63973308447624725004288
> 37: 671389 313519863989706816307303809024
> 38: 182549 45225850656203876163438682112
> 39: 1336282 31933986316064959928909955072
> 40: 18049 6034750858947540643601186816
> 41: 1289210 4145806855637690163777954119680
> 42: 634402 143410752413726318705389116325888
> 43: 2679419 251570201273324198920857495653056512
> 44: 156629 9442738596003761319219036160
> 45: 3428818 288049927140258932406824739012608
> 46: 987498 20384387023837630566380055072075677696
> 47: 5876576 16579286652350303184601394767032483840
> 48: 13308 152556272234873601963528260943872
> 49: 8122478 463424116819682991065891465214793542008832
> 50: 3118809 63039435236897106221986787164071919616
> 51: 14743535 247126135557931098912701316497011638272
> 52: 796352 1083181655178944127338714024967634157568
> 53: 15921180 71286088956163866149580753955553592475648
> 54: 4952057 2150676694930424720837752491965232971776
> 55: 29170111 507477067298501219491044453334717130866688
> 56: 403964 1746977513106742264740052226757623808
> 57: 48839762 27320774362755367988623371083844092646391808
> 58: 11997500 6094365163190490383475585992644805477269504
> 59: 71116907 9188495794580645540482153719631435565136609280
> 60: 2675259 14463684581762047084433709884282673037312
> 61: 122451245 9107655699502841924691980127153411750800769679360
> 62: 17820844 199082515611433949561498862265902993781030912
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Wed Feb  4 01:36:17 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 3 Feb 2015 19:36:17 -0500
Subject: [seqfan] Re: A113917 and A113918: zero-free squaring
In-Reply-To: <CAAOnSgRCE4f0Bj5ADpt2nQjufdYz_j_69E+vaVp_SbJm85O4SA@mail.gmail.com>
References: <201502031734.t13HYwP09486@crypt.org>
 <CAAOnSgRCE4f0Bj5ADpt2nQjufdYz_j_69E+vaVp_SbJm85O4SA@mail.gmail.com>
Message-ID: <CAAOnSgQL8D43Hw1c3Rvy6O88Y36ba1cG=5Eh2AcntidgNRgdQw@mail.gmail.com>

Hugo, Is what I meant to say...

Hugo,   certainly those two sequences are worth adding
to the OEIS! Please do so!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Feb 3, 2015 at 7:33 PM, Neil Sloane <njasloane at gmail.com> wrote:

> Hans, certainly those two sequences are worth adding
> to the OEIS! Please do so!
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Tue, Feb 3, 2015 at 12:34 PM, <hv at crypt.org> wrote:
>
>> Back in Jan 2006, David Wilson introduced this question:
>>
>>   For a number n, let f(n) be the set of numbers gotten by splitting n^2
>> at
>>   the 0 digits.  For example
>>
>>   29648^2 = 879003904
>>
>>   so f(29648) = { 4, 39, 879 }
>>
>>   Let S be the smallest set of numbers containing 2 and fixed by f.  What
>> is
>>   the largest element of S?
>>
>> .. which eventually gave A113917 (largest element) and A113918
>> (cardinality
>> of the set).
>>
>> I did say at the time "I don't have full confidence in the results", but
>> when trying to clean up my 2006 code recently, as part of a long-running
>> project to push all my maths code to Github, I found several bugs which
>> meant some of the results were wrong. Sorry about that.
>>
>> I've fixed those and further improved the code, available under 'zerofree'
>> in <https://github.com/hvds/seq>, and will go update the sequences on
>> the assumption that my new code is correct. I'd still appreciate it if
>> someone could confirm some or all of the values though.
>>
>> I estimate the cardinality for A113918(9) is between 10^10 and 10^13,
>> which I can't calculate with my current approach (but I have another
>> approach in mind that might reach it). Given the rate of growth, I think
>> n=10 (ie the original question) is likely to be beyond my means.
>>
>> With the new code it's easy to change the calculation, and replacing
>> s -> s^2 with s -> 2s gives a new pair of sequences that grows slow enough
>> it's easy to calculate more terms; I'm not sure if they're also worth
>> adding to OEIS, or if there are different calculations that would also be
>> of interest.
>>
>> Hugo
>> ---
>> With calculation s -> s^2: "n: card(n) max(n)"
>> 2: 2 2
>> 3: 18 1849
>> 4: 2 2
>> 5: 3050 266423227914725931
>> 6: 34762 3100840870711697060720215047
>> 7: 3087549 845486430620513036335402848567278325780455810752216401
>> 8: 2 4
>>
>> With calculation s -> 2s: "n: card(n) max(n)"
>> 2: 2 2
>> 3: 6 16
>> 4: 2 2
>> 5: 20 192
>> 6: 13 128
>> 7: 72 32768
>> 8: 3 4
>> 9: 92 69632
>> 10: 42 23552
>> 11: 308 25722880
>> 12: 34 425984
>> 13: 900 717895680
>> 14: 178 1051828224
>> 15: 1739 217079873536
>> 16: 4 8
>> 17: 3349 2270641389568
>> 18: 443 10603200512
>> 19: 4523 156423849771008
>> 20: 387 950175531008
>> 21: 14364 25160124578398208
>> 22: 1827 385584983965696
>> 23: 18672 450589122059304960
>> 24: 234 40722497536
>> 25: 39426 53279734579488838656
>> 26: 15882 127148822502119047168
>> 27: 52664 299326717942059499520
>> 28: 8858 43157851113903387312128
>> 29: 128253 13526981441472537034752
>> 30: 28346 449522648486053412864
>> 31: 123087 371244129204723018366976
>> 32: 5 16
>> 33: 259207 23655711299608586448011264
>> 34: 87797 103182870656711001112576
>> 35: 363512 39823687474383259120435200
>> 36: 44545 63973308447624725004288
>> 37: 671389 313519863989706816307303809024
>> 38: 182549 45225850656203876163438682112
>> 39: 1336282 31933986316064959928909955072
>> 40: 18049 6034750858947540643601186816
>> 41: 1289210 4145806855637690163777954119680
>> 42: 634402 143410752413726318705389116325888
>> 43: 2679419 251570201273324198920857495653056512
>> 44: 156629 9442738596003761319219036160
>> 45: 3428818 288049927140258932406824739012608
>> 46: 987498 20384387023837630566380055072075677696
>> 47: 5876576 16579286652350303184601394767032483840
>> 48: 13308 152556272234873601963528260943872
>> 49: 8122478 463424116819682991065891465214793542008832
>> 50: 3118809 63039435236897106221986787164071919616
>> 51: 14743535 247126135557931098912701316497011638272
>> 52: 796352 1083181655178944127338714024967634157568
>> 53: 15921180 71286088956163866149580753955553592475648
>> 54: 4952057 2150676694930424720837752491965232971776
>> 55: 29170111 507477067298501219491044453334717130866688
>> 56: 403964 1746977513106742264740052226757623808
>> 57: 48839762 27320774362755367988623371083844092646391808
>> 58: 11997500 6094365163190490383475585992644805477269504
>> 59: 71116907 9188495794580645540482153719631435565136609280
>> 60: 2675259 14463684581762047084433709884282673037312
>> 61: 122451245 9107655699502841924691980127153411750800769679360
>> 62: 17820844 199082515611433949561498862265902993781030912
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>


From hv at crypt.org  Wed Feb  4 02:52:19 2015
From: hv at crypt.org (hv at crypt.org)
Date: Wed, 04 Feb 2015 01:52:19 +0000
Subject: [seqfan] Re: A113917 and A113918: zero-free squaring
In-Reply-To: <CAAOnSgQL8D43Hw1c3Rvy6O88Y36ba1cG=5Eh2AcntidgNRgdQw@mail.gmail.com> 
Message-ID: <201502040152.t141qJP10329@crypt.org>

Now proposed as A254637, A254638.

(Given it's otherwise the same code as discussed below for A113917/8, maybe
this would be a better example for someone else to confirm.)

Hugo

Neil Sloane <njasloane at gmail.com> wrote:
:Hugo, Is what I meant to say...
:
:Hugo,   certainly those two sequences are worth adding
:to the OEIS! Please do so!
:
:Best regards
:Neil
:
:Neil J. A. Sloane, President, OEIS Foundation.
:11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
:Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
:Phone: 732 828 6098; home page: http://NeilSloane.com
:Email: njasloane at gmail.com
:
:
:On Tue, Feb 3, 2015 at 7:33 PM, Neil Sloane <njasloane at gmail.com> wrote:
:
:> Hans, certainly those two sequences are worth adding
:> to the OEIS! Please do so!
:>
:> Best regards
:> Neil
:>
:> Neil J. A. Sloane, President, OEIS Foundation.
:> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
:> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
:> Phone: 732 828 6098; home page: http://NeilSloane.com
:> Email: njasloane at gmail.com
:>
:>
:> On Tue, Feb 3, 2015 at 12:34 PM, <hv at crypt.org> wrote:
:>
:>> Back in Jan 2006, David Wilson introduced this question:
:>>
:>>   For a number n, let f(n) be the set of numbers gotten by splitting n^2
:>> at
:>>   the 0 digits.  For example
:>>
:>>   29648^2 = 879003904
:>>
:>>   so f(29648) = { 4, 39, 879 }
:>>
:>>   Let S be the smallest set of numbers containing 2 and fixed by f.  What
:>> is
:>>   the largest element of S?
:>>
:>> .. which eventually gave A113917 (largest element) and A113918
:>> (cardinality
:>> of the set).
:>>
:>> I did say at the time "I don't have full confidence in the results", but
:>> when trying to clean up my 2006 code recently, as part of a long-running
:>> project to push all my maths code to Github, I found several bugs which
:>> meant some of the results were wrong. Sorry about that.
:>>
:>> I've fixed those and further improved the code, available under 'zerofree'
:>> in <https://github.com/hvds/seq>, and will go update the sequences on
:>> the assumption that my new code is correct. I'd still appreciate it if
:>> someone could confirm some or all of the values though.
:>>
:>> I estimate the cardinality for A113918(9) is between 10^10 and 10^13,
:>> which I can't calculate with my current approach (but I have another
:>> approach in mind that might reach it). Given the rate of growth, I think
:>> n=10 (ie the original question) is likely to be beyond my means.
:>>
:>> With the new code it's easy to change the calculation, and replacing
:>> s -> s^2 with s -> 2s gives a new pair of sequences that grows slow enough
:>> it's easy to calculate more terms; I'm not sure if they're also worth
:>> adding to OEIS, or if there are different calculations that would also be
:>> of interest.
:>>
:>> Hugo
:>> ---
:>> With calculation s -> s^2: "n: card(n) max(n)"
:>> 2: 2 2
:>> 3: 18 1849
:>> 4: 2 2
:>> 5: 3050 266423227914725931
:>> 6: 34762 3100840870711697060720215047
:>> 7: 3087549 845486430620513036335402848567278325780455810752216401
:>> 8: 2 4
:>>
:>> With calculation s -> 2s: "n: card(n) max(n)"
:>> 2: 2 2
:>> 3: 6 16
:>> 4: 2 2
:>> 5: 20 192
:>> 6: 13 128
:>> 7: 72 32768
:>> 8: 3 4
:>> 9: 92 69632
:>> 10: 42 23552
:>> 11: 308 25722880
:>> 12: 34 425984
:>> 13: 900 717895680
:>> 14: 178 1051828224
:>> 15: 1739 217079873536
:>> 16: 4 8
:>> 17: 3349 2270641389568
:>> 18: 443 10603200512
:>> 19: 4523 156423849771008
:>> 20: 387 950175531008
:>> 21: 14364 25160124578398208
:>> 22: 1827 385584983965696
:>> 23: 18672 450589122059304960
:>> 24: 234 40722497536
:>> 25: 39426 53279734579488838656
:>> 26: 15882 127148822502119047168
:>> 27: 52664 299326717942059499520
:>> 28: 8858 43157851113903387312128
:>> 29: 128253 13526981441472537034752
:>> 30: 28346 449522648486053412864
:>> 31: 123087 371244129204723018366976
:>> 32: 5 16
:>> 33: 259207 23655711299608586448011264
:>> 34: 87797 103182870656711001112576
:>> 35: 363512 39823687474383259120435200
:>> 36: 44545 63973308447624725004288
:>> 37: 671389 313519863989706816307303809024
:>> 38: 182549 45225850656203876163438682112
:>> 39: 1336282 31933986316064959928909955072
:>> 40: 18049 6034750858947540643601186816
:>> 41: 1289210 4145806855637690163777954119680
:>> 42: 634402 143410752413726318705389116325888
:>> 43: 2679419 251570201273324198920857495653056512
:>> 44: 156629 9442738596003761319219036160
:>> 45: 3428818 288049927140258932406824739012608
:>> 46: 987498 20384387023837630566380055072075677696
:>> 47: 5876576 16579286652350303184601394767032483840
:>> 48: 13308 152556272234873601963528260943872
:>> 49: 8122478 463424116819682991065891465214793542008832
:>> 50: 3118809 63039435236897106221986787164071919616
:>> 51: 14743535 247126135557931098912701316497011638272
:>> 52: 796352 1083181655178944127338714024967634157568
:>> 53: 15921180 71286088956163866149580753955553592475648
:>> 54: 4952057 2150676694930424720837752491965232971776
:>> 55: 29170111 507477067298501219491044453334717130866688
:>> 56: 403964 1746977513106742264740052226757623808
:>> 57: 48839762 27320774362755367988623371083844092646391808
:>> 58: 11997500 6094365163190490383475585992644805477269504
:>> 59: 71116907 9188495794580645540482153719631435565136609280
:>> 60: 2675259 14463684581762047084433709884282673037312
:>> 61: 122451245 9107655699502841924691980127153411750800769679360
:>> 62: 17820844 199082515611433949561498862265902993781030912
:>>
:>>
:>> _______________________________________________
:>>
:>> Seqfan Mailing list - http://list.seqfan.eu/
:>>
:>
:>
:
:_______________________________________________
:
:Seqfan Mailing list - http://list.seqfan.eu/


From maxale at gmail.com  Wed Feb  4 03:06:14 2015
From: maxale at gmail.com (Max Alekseyev)
Date: Tue, 3 Feb 2015 21:06:14 -0500
Subject: [seqfan] self-referential forms
Message-ID: <CAJkPp5PBaxzLRz51L27YevxjnG90HW1cKM1Fg2FoW2vfBGK6dA@mail.gmail.com>

SeqFans,

I've recently tried to formalize and give some counts for the question
on self-referential forms at MathOverflow:
http://mathoverflow.net/questions/194905/compiling-self-referential-forms
In particular, I computed two sequences there, which may be considered
for addition to the OIES.
I'm however not sure if they are motivated enough and not too special
for the general interest. So I'd like to know your opinion in this
respect.

Regards,
Max


From njasloane at gmail.com  Wed Feb  4 04:03:31 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 3 Feb 2015 22:03:31 -0500
Subject: [seqfan] Re: self-referential forms
In-Reply-To: <CAJkPp5PBaxzLRz51L27YevxjnG90HW1cKM1Fg2FoW2vfBGK6dA@mail.gmail.com>
References: <CAJkPp5PBaxzLRz51L27YevxjnG90HW1cKM1Fg2FoW2vfBGK6dA@mail.gmail.com>
Message-ID: <CAAOnSgQ-zd7NBNqzikasoFpW9Rz7Dz7La1t28nf3hNLEWG82rg@mail.gmail.com>

Max, Those sequences have 3 things going for them
- they were created by one of the best contributors
to the OEIS (you), they are on the web, and at least one
other person on math overflow is interested in them.

So, yes, definitely submit them

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Feb 3, 2015 at 9:06 PM, Max Alekseyev <maxale at gmail.com> wrote:

> SeqFans,
>
> I've recently tried to formalize and give some counts for the question
> on self-referential forms at MathOverflow:
> http://mathoverflow.net/questions/194905/compiling-self-referential-forms
> In particular, I computed two sequences there, which may be considered
> for addition to the OIES.
> I'm however not sure if they are motivated enough and not too special
> for the general interest. So I'd like to know your opinion in this
> respect.
>
> Regards,
> Max
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From ixitol at gmail.com  Wed Feb  4 06:33:57 2015
From: ixitol at gmail.com (Russell Walsmith)
Date: Tue, 3 Feb 2015 21:33:57 -0800
Subject: [seqfan] A sequence of sequence-generating matrices
Message-ID: <CAOPCv-XEsNTn_dv=5kTyc-J5K-t0C=ZpeNEz8k2=Fy9DOhNW+Q@mail.gmail.com>

Exploring different numerical sequences* generated by a certain 3 x 3
matrix, I found it to be part of an n x n family with a similar, though
increasingly complex, form. I've discovered six entries in this sequence of
matrices so far... does anyone see where it goes from here...?

http://ixitol.com/MatrixSequence

* (e.g., A249578 <https://oeis.org/A249578>, A249579
<https://oeis.org/A249579>, A249580 <https://oeis.org/A249580>...)


From penson at lptmc.jussieu.fr  Wed Feb  4 20:01:38 2015
From: penson at lptmc.jussieu.fr (Karol A. Penson)
Date: Wed, 04 Feb 2015 20:01:38 +0100
Subject: [seqfan]  Re: Question on A005572 from K. A. Penson
In-Reply-To: <Prayer.1.3.5.1502021746310.15725@viol.math.ubc.ca>
References: <54D00718.50007@lptl.jussieu.fr>
 <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>
 <Prayer.1.3.5.1502021746310.15725@viol.math.ubc.ca>
Message-ID: <54D26C92.9040708@lptmc.jussieu.fr>

  Re: A005572

I thank Max Alekseyev, Robert Israel and Paul Hanna for important remarks.
Robert's compact form can be further transformed using formula 
8.3.2.135, ch.8, p.666
  of  Yury A. Brychkov, "Handbook of Special Functions, Derivatives, 
Integrals, Series and Other Formulas",
(CRC Press, Taylor and Francis, New York, 2008),
and the following relation obtains using  the classical Gegenbauer 
polynomials, in Maple notation:

  A005572(n)=2*(12^(n/2))*(n!/(n+2)!)*GegenbauerC(n, 3/2, 2/sqrt(3)), 
n=0,1... .

Robert, would you like to enter your formula; I will then enter my 
Gegenbauer version.

Best,


Karol A. Penson






Le 03/02/2015 02:46, israel at math.ubc.ca a ?crit :
> And, according to Maple, these sums can be written as a hypergeometric 
> function:
>
> A005572(n) = 4^n*hypergeom([-n/2, (1-n)/2], [2], 1/4)
>
> Cheers,
> Robert
>
> On Feb 2 2015, Max Alekseyev wrote:
>
>> Hi Karol,
>>
>> There is a formula
>>
>> A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,
>>
>> which expands (with substitution k -> n-2k) into:
>>
>> A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
>> (k+1) * 4^(n-2k)
>>
>> PARI/GP code:
>>
>> { A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
>> * 4^(n-2*k) ) }
>>
>> Regards,
>> Max
>>
>>
>>
>> On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
>>> Does anybody know how to obtain the close form of A005572(n) ?
>>>
>>> Thanking in advance,
>>>
>>>     Karol A. Penson
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



From israel at math.ubc.ca  Wed Feb  4 22:40:06 2015
From: israel at math.ubc.ca (israel at math.ubc.ca)
Date: 04 Feb 2015 13:40:06 -0800
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
In-Reply-To: <54D26C92.9040708@lptmc.jussieu.fr>
References: <54D00718.50007@lptl.jussieu.fr>
 <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>
 <Prayer.1.3.5.1502021746310.15725@viol.math.ubc.ca>
 <54D26C92.9040708@lptmc.jussieu.fr>
Message-ID: <Prayer.1.3.5.1502041340060.29479@viol.math.ubc.ca>

Done.  I note that Peter Luschny has also entered a different
hypergeometric form.  I don't know how that one was derived.

Cheers,
Robert

On Feb 4 2015, Karol A. Penson wrote:

>  Re: A005572
>
>I thank Max Alekseyev, Robert Israel and Paul Hanna for important remarks.
>Robert's compact form can be further transformed using formula 
>8.3.2.135, ch.8, p.666
>  of  Yury A. Brychkov, "Handbook of Special Functions, Derivatives, 
>Integrals, Series and Other Formulas",
>(CRC Press, Taylor and Francis, New York, 2008),
>and the following relation obtains using  the classical Gegenbauer 
>polynomials, in Maple notation:
>
>  A005572(n)=2*(12^(n/2))*(n!/(n+2)!)*GegenbauerC(n, 3/2, 2/sqrt(3)), 
>n=0,1... .
>
>Robert, would you like to enter your formula; I will then enter my 
>Gegenbauer version.
>
>Best,
>
>
>Karol A. Penson
>
>
>
>
>
>
>Le 03/02/2015 02:46, israel at math.ubc.ca a ?crit :
>> And, according to Maple, these sums can be written as a hypergeometric 
>> function:
>>
>> A005572(n) = 4^n*hypergeom([-n/2, (1-n)/2], [2], 1/4)
>>
>> Cheers,
>> Robert
>>
>> On Feb 2 2015, Max Alekseyev wrote:
>>
>>> Hi Karol,
>>>
>>> There is a formula
>>>
>>> A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,
>>>
>>> which expands (with substitution k -> n-2k) into:
>>>
>>> A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
>>> (k+1) * 4^(n-2k)
>>>
>>> PARI/GP code:
>>>
>>> { A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
>>> * 4^(n-2*k) ) }
>>>
>>> Regards,
>>> Max
>>>
>>>
>>>
>>> On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
>>>> Does anybody know how to obtain the close form of A005572(n) ?
>>>>
>>>> Thanking in advance,
>>>>
>>>>     Karol A. Penson
>>>>
>>>> _______________________________________________
>>>>
>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>



From mathar at mpia-hd.mpg.de  Thu Feb  5 20:08:28 2015
From: mathar at mpia-hd.mpg.de (Richard J. Mathar)
Date: Thu, 5 Feb 2015 20:08:28 +0100
Subject: [seqfan] g.f. in A157143
Message-ID: <20150205190828.GA14851@mathar.mpia-hd.mpg.de>

Is the generating function in A157143 correct?
The Maple lines
 cx := (1-sqrt(1-4*x))/(2*x) ;
 gx := subs(x=(x/(1+x^2+x^3))^2,cx)*(1-x)/(1+x^2+x^3) ;
 series(%,x=0,50) ;
 gfun[seriestolist](%) ;

based on the A000108 g.f.  generate
1, -1, 0, -1, 1, -1, 2, -2, 4, -5, 8, -13, 18, -32, 46, -77, 123, -192, 325,..

and the 
 mx := (1-x-sqrt(1-2*x-3*x^2))/(2*x^2) ;
 gx := subs(x=(x/(1+x^2+x^3))^2,mx)*(1-x)/(1+x^2+x^3) ;
 series(%,x=0,50) ;
 gfun[seriestolist](%) ;

based on the A000106 (assuming a typo in the formula) g.f. gives
1, -1, 0, -1, 1, -1, 1, -1, 6, 0, -3, -20, 10, 20, 20, -84, -3, 135, 228
and both don't match.


From rselcoe at entouchonline.net  Sat Feb  7 22:01:47 2015
From: rselcoe at entouchonline.net (Bob Selcoe)
Date: Sat, 7 Feb 2015 15:01:47 -0600
Subject: [seqfan] Question re: A250000
In-Reply-To: <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
References: <9822A525B8DE44D79AD6E4E13405CEB9@OwnerPC>
 <CAAcpPSYqW=bvyWt2Nbm1-67etMVnKEYwQjX0q9DNRNbQ5831JA@mail.gmail.com>
 <54AEBE97.9020305@brennen.net> <88684506471F4A2FA027EEC93A2D771E@OwnerPC>
 <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
Message-ID: <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC>


Hello Seqfans,

The sequence A250000 (maximum number of peacefully coexisting equal-sized 
"armies" of queens on chess boards of varying n X n sizes) poses some 
fascinating problems.

The length of the sequence is small; only up to a(13) = 24.

The "known" lower bound for a solution is a(n) = 9/64*n^2. There is a link 
to a paper by Prestwich and Beck referenced in the sequence which expands on 
this idea.  I can't follow the paper, but it apparently provides an upper 
bound, as well.

For all n = 4m+1 m>=0, I can show a pattern of quasi-symmetric queen 
placement such that a(n) = 2m(m+1).  For m = {0..3}, this is indeed the 
maximum number of queens possible.  For m>=4, these solutions are < the 
known lower bound of (9/64)*n^2.

I have proposed for A250000 examples of solutions using this queen pattern 
for n=9 and n=13.  Please refer to the sequence history to see the pattern. 
Since the pattern yields 40 for n=17, and a(17)=42 is the known lower bound, 
it (apparently) does not provide a solution for a(17).

Can anyone show an actual example of a 17 X 17 chessboard where the number 
of queens > 40, even if it can't be proven to be a solution (maximum number 
of queens) for a(17)?

Best Wishes,
Bob Selcoe
 



From Rob.Pratt at sas.com  Sat Feb  7 23:17:51 2015
From: Rob.Pratt at sas.com (Rob Pratt)
Date: Sat, 7 Feb 2015 22:17:51 +0000
Subject: [seqfan] Re: Question re: A250000
In-Reply-To: <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC>
References: <9822A525B8DE44D79AD6E4E13405CEB9@OwnerPC>
 <CAAcpPSYqW=bvyWt2Nbm1-67etMVnKEYwQjX0q9DNRNbQ5831JA@mail.gmail.com>
 <54AEBE97.9020305@brennen.net> <88684506471F4A2FA027EEC93A2D771E@OwnerPC>
 <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
 <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC>
Message-ID: <f9754f2d350443cab54d2ed30870ac5e@MERCMBX38D.na.SAS.com>

Here's a 17x17 solution with 42 queens of each color:



1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

1

W

W

W

W

W

2

W

W

W

W

W

3

W

W

W

W

W

W

4

W

W

W

W

W

W

5

W

W

W

W

W

W

6

W

W

W

W

W

7

W

W

W

W

8

W

W

W

9

W

W

10

B

B

11

B

B

B

12

B

B

B

B

13

B

B

B

B

B

14

B

B

B

B

B

B

B

15

B

B

B

B

B

B

B

B

16

B

B

B

B

B

B

B

17

B

B

B

B

B

B






-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Bob Selcoe
Sent: Saturday, February 07, 2015 4:02 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Question re: A250000





Hello Seqfans,



The sequence A250000 (maximum number of peacefully coexisting equal-sized "armies" of queens on chess boards of varying n X n sizes) poses some fascinating problems.



The length of the sequence is small; only up to a(13) = 24.



The "known" lower bound for a solution is a(n) = 9/64*n^2. There is a link to a paper by Prestwich and Beck referenced in the sequence which expands on this idea.  I can't follow the paper, but it apparently provides an upper bound, as well.



For all n = 4m+1 m>=0, I can show a pattern of quasi-symmetric queen placement such that a(n) = 2m(m+1).  For m = {0..3}, this is indeed the maximum number of queens possible.  For m>=4, these solutions are < the known lower bound of (9/64)*n^2.



I have proposed for A250000 examples of solutions using this queen pattern for n=9 and n=13.  Please refer to the sequence history to see the pattern.

Since the pattern yields 40 for n=17, and a(17)=42 is the known lower bound, it (apparently) does not provide a solution for a(17).



Can anyone show an actual example of a 17 X 17 chessboard where the number of queens > 40, even if it can't be proven to be a solution (maximum number of queens) for a(17)?



Best Wishes,

Bob Selcoe





_______________________________________________



Seqfan Mailing list - http://list.seqfan.eu/

From Eric.Angelini at kntv.be  Sat Feb  7 23:23:29 2015
From: Eric.Angelini at kntv.be (Eric Angelini)
Date: Sat, 7 Feb 2015 23:23:29 +0100
Subject: [seqfan] Absolute diff and sums not to be shared
Message-ID: <8B00BFBA136BAB43AD27F9EDC3758F03B571C46625@KNTVSRV01.kntv.local>

Hello SeqFans,
We want S to be a permutation of the integers >0;
We want S to be the lexicographically first seq of its kind (see below);
If we take two adjacent integers of S, say p & q, we want that:
-> no other pair of adjacent integers in S shares the abs. diff. |p-q|
-> no other pair of adjacent integers in S shares the sum (p+q)
-> no |p-q|=(p'+q') with p'and q' being two other adjacent integers in S.

So S is extended with the smallest integer n such that neither |(n-1)-n|
nor [(n-1)+n] has occurred before as a sum or as a diff. of two adjacent
integers in S.

  Sum  3  6  12 11 13  28  27 32  29 22
S(n)= 1  2  4  8  3  10  18  9  23  6  16 ...
  Dif  1  2  4  5  7   8   9  14  17 10

Hope this is not old hat,
Best,
?.


From reinhard.zumkeller at gmail.com  Sun Feb  8 00:49:11 2015
From: reinhard.zumkeller at gmail.com (Reinhard Zumkeller)
Date: Sun, 8 Feb 2015 00:49:11 +0100
Subject: [seqfan] Re: Absolute diff and sums not to be shared
In-Reply-To: <8B00BFBA136BAB43AD27F9EDC3758F03B571C46625@KNTVSRV01.kntv.local>
References: <8B00BFBA136BAB43AD27F9EDC3758F03B571C46625@KNTVSRV01.kntv.local>
Message-ID: <CAOyfccivTmKye4LLgwHcyC4_mQoS5wZhbZ9Xs7xTR3kJm4tSwA@mail.gmail.com>

see https://oeis.org/draft/A254788

Best, Reinhard

2015-02-07 23:23 GMT+01:00 Eric Angelini <Eric.Angelini at kntv.be>:

> Hello SeqFans,
> We want S to be a permutation of the integers >0;
> We want S to be the lexicographically first seq of its kind (see below);
> If we take two adjacent integers of S, say p & q, we want that:
> -> no other pair of adjacent integers in S shares the abs. diff. |p-q|
> -> no other pair of adjacent integers in S shares the sum (p+q)
> -> no |p-q|=(p'+q') with p'and q' being two other adjacent integers in S.
>
> So S is extended with the smallest integer n such that neither |(n-1)-n|
> nor [(n-1)+n] has occurred before as a sum or as a diff. of two adjacent
> integers in S.
>
>   Sum  3  6  12 11 13  28  27 32  29 22
> S(n)= 1  2  4  8  3  10  18  9  23  6  16 ...
>   Dif  1  2  4  5  7   8   9  14  17 10
>
> Hope this is not old hat,
> Best,
> ?.
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From Rob.Pratt at sas.com  Sun Feb  8 04:43:30 2015
From: Rob.Pratt at sas.com (Rob Pratt)
Date: Sun, 8 Feb 2015 03:43:30 +0000
Subject: [seqfan] Re: Question re: A250000
References: <9822A525B8DE44D79AD6E4E13405CEB9@OwnerPC>
 <CAAcpPSYqW=bvyWt2Nbm1-67etMVnKEYwQjX0q9DNRNbQ5831JA@mail.gmail.com>
 <54AEBE97.9020305@brennen.net> <88684506471F4A2FA027EEC93A2D771E@OwnerPC>
 <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
 <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC> 
Message-ID: <bf66abc63f7045e49bff4526b491108e@MERCMBX38D.na.SAS.com>

Here it is with unoccupied squares indicated with dots (view with a fixed-width font):

....WWWWW........
....WWWWW........
....WWWWW.......W
....WWWW.......WW
....WWW.......WWW
.....W.......WWWW
.............WWWW
.............WWW.
.............WW..
..BB.............
.BBB.............
BBBB.............
BBBB.......B.....
BBBB......BBB....
BBBB.....BBBB....
BBB......BBBB....
BB.......BBBB....

From: Rob Pratt
Sent: Saturday, February 07, 2015 5:18 PM
To: Sequence Fanatics Discussion list
Subject: RE: [seqfan] Question re: A250000


Here's a 17x17 solution with 42 queens of each color:



1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

1

W

W

W

W

W

2

W

W

W

W

W

3

W

W

W

W

W

W

4

W

W

W

W

W

W

5

W

W

W

W

W

W

6

W

W

W

W

W

7

W

W

W

W

8

W

W

W

9

W

W

10

B

B

11

B

B

B

12

B

B

B

B

13

B

B

B

B

B

14

B

B

B

B

B

B

B

15

B

B

B

B

B

B

B

B

16

B

B

B

B

B

B

B

17

B

B

B

B

B

B






-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Bob Selcoe
Sent: Saturday, February 07, 2015 4:02 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Question re: A250000





Hello Seqfans,



The sequence A250000 (maximum number of peacefully coexisting equal-sized "armies" of queens on chess boards of varying n X n sizes) poses some fascinating problems.



The length of the sequence is small; only up to a(13) = 24.



The "known" lower bound for a solution is a(n) = 9/64*n^2. There is a link to a paper by Prestwich and Beck referenced in the sequence which expands on this idea.  I can't follow the paper, but it apparently provides an upper bound, as well.



For all n = 4m+1 m>=0, I can show a pattern of quasi-symmetric queen placement such that a(n) = 2m(m+1).  For m = {0..3}, this is indeed the maximum number of queens possible.  For m>=4, these solutions are < the known lower bound of (9/64)*n^2.



I have proposed for A250000 examples of solutions using this queen pattern for n=9 and n=13.  Please refer to the sequence history to see the pattern.

Since the pattern yields 40 for n=17, and a(17)=42 is the known lower bound, it (apparently) does not provide a solution for a(17).



Can anyone show an actual example of a 17 X 17 chessboard where the number of queens > 40, even if it can't be proven to be a solution (maximum number of queens) for a(17)?



Best Wishes,

Bob Selcoe







_______________________________________________



Seqfan Mailing list - http://list.seqfan.eu/

From rselcoe at entouchonline.net  Sun Feb  8 07:52:14 2015
From: rselcoe at entouchonline.net (Bob Selcoe)
Date: Sun, 8 Feb 2015 00:52:14 -0600
Subject: [seqfan] Re: Question re: A250000
In-Reply-To: <bf66abc63f7045e49bff4526b491108e@MERCMBX38D.na.SAS.com>
References: <9822A525B8DE44D79AD6E4E13405CEB9@OwnerPC>
 <CAAcpPSYqW=bvyWt2Nbm1-67etMVnKEYwQjX0q9DNRNbQ5831JA@mail.gmail.com>
 <54AEBE97.9020305@brennen.net> <88684506471F4A2FA027EEC93A2D771E@OwnerPC>
 <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
 <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC>
 <bf66abc63f7045e49bff4526b491108e@MERCMBX38D.na.SAS.com>
Message-ID: <EB99758CBECB48E9A1DC4FFB6FC6C060@OwnerPC>

Hi again Rob an others,

And  two more 42-queen variations for n=17:

Alternative 1:

.....WWWWW.......
.....WWWWW.......
.....WWWWW......W
.....WWWW......WW
.....WWW......WWW
......W......WWWW
.............WWWW
.............WWW.
.............WW..
...BB............
..BBB............
.BBBB............
BBBBB......BB....
BBBBB.....BBB....
BBBB......BBB....
BBB.......BBB....
BB........BBB....



Alternative 2:

....WWWW........W
....WWWW.......WW
....WWWW......WWW
....WWWW.....WWWW
.....WW......WWWW
.............WWWW
.............WWW.
.............WW..
.............W...
..BB.............
.BBB.............
BBBB.......B.....
BBBB......BBB....
BBB......BBBB....
BB......BBBBB....
B.......BBBBB....
........BBBBB....


The symmetry of the W-blocks and the quasi-symmetry of the B-blocks for the 
second example surprises me.

I wonder if there are any solutions for a(n) > floor_(9n^2/64) for any n?

Cheers,
Bob S


--------------------------------------------------
From: "Rob Pratt" <Rob.Pratt at sas.com>
Sent: Saturday, February 07, 2015 9:43 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Question re: A250000

> Here it is with unoccupied squares indicated with dots (view with a 
> fixed-width font):
>
> ....WWWWW........
> ....WWWWW........
> ....WWWWW.......W
> ....WWWW.......WW
> ....WWW.......WWW
> .....W.......WWWW
> .............WWWW
> .............WWW.
> .............WW..
> ..BB.............
> .BBB.............
> BBBB.............
> BBBB.......B.....
> BBBB......BBB....
> BBBB.....BBBB....
> BBB......BBBB....
> BB.......BBBB....
>
> From: Rob Pratt
> Sent: Saturday, February 07, 2015 5:18 PM
> To: Sequence Fanatics Discussion list
> Subject: RE: [seqfan] Question re: A250000
>
>
> Here's a 17x17 solution with 42 queens of each color:
>
>
>
> 1
>
> 2
>
> 3
>
> 4
>
> 5
>
> 6
>
> 7
>
> 8
>
> 9
>
> 10
>
> 11
>
> 12
>
> 13
>
> 14
>
> 15
>
> 16
>
> 17
>
> 1
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 2
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 3
>
> W
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 4
>
> W
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 5
>
> W
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 6
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 7
>
> W
>
> W
>
> W
>
> W
>
> 8
>
> W
>
> W
>
> W
>
> 9
>
> W
>
> W
>
> 10
>
> B
>
> B
>
> 11
>
> B
>
> B
>
> B
>
> 12
>
> B
>
> B
>
> B
>
> B
>
> 13
>
> B
>
> B
>
> B
>
> B
>
> B
>
> 14
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> 15
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> 16
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> 17
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
>
>
>
>
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Bob 
> Selcoe
> Sent: Saturday, February 07, 2015 4:02 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Question re: A250000
>
>
>
>
>
> Hello Seqfans,
>
>
>
> The sequence A250000 (maximum number of peacefully coexisting equal-sized 
> "armies" of queens on chess boards of varying n X n sizes) poses some 
> fascinating problems.
>
>
>
> The length of the sequence is small; only up to a(13) = 24.
>
>
>
> The "known" lower bound for a solution is a(n) = 9/64*n^2. There is a link 
> to a paper by Prestwich and Beck referenced in the sequence which expands 
> on this idea.  I can't follow the paper, but it apparently provides an 
> upper bound, as well.
>
>
>
> For all n = 4m+1 m>=0, I can show a pattern of quasi-symmetric queen 
> placement such that a(n) = 2m(m+1).  For m = {0..3}, this is indeed the 
> maximum number of queens possible.  For m>=4, these solutions are < the 
> known lower bound of (9/64)*n^2.
>
>
>
> I have proposed for A250000 examples of solutions using this queen pattern 
> for n=9 and n=13.  Please refer to the sequence history to see the 
> pattern.
>
> Since the pattern yields 40 for n=17, and a(17)=42 is the known lower 
> bound, it (apparently) does not provide a solution for a(17).
>
>
>
> Can anyone show an actual example of a 17 X 17 chessboard where the number 
> of queens > 40, even if it can't be proven to be a solution (maximum 
> number of queens) for a(17)?
>
>
>
> Best Wishes,
>
> Bob Selcoe
>
>
>
>
>
>
>
> _______________________________________________
>
>
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
> 


From andrew.weimholt at gmail.com  Mon Feb  9 10:29:53 2015
From: andrew.weimholt at gmail.com (Andrew Weimholt)
Date: Mon, 9 Feb 2015 01:29:53 -0800
Subject: [seqfan] A027624 initial term
Message-ID: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>

Hi,

I believe the first term of A027624 should be 2, not 1.

The history shows that Eric W. Weisstein was going to make such a
"correction" a while back, but then changed his mind and backed out the
change.

Can anyone offer an explanation?

Andrew


From franktaw at netscape.net  Mon Feb  9 11:12:26 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Mon, 9 Feb 2015 05:12:26 -0500
Subject: [seqfan] Re: A027624 initial term
In-Reply-To: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>
References: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>
Message-ID: <8D212680A1EAF46-13DC-37227@webmail-va003.sysops.aol.com>

There's the fact that the formula in the definition evaluates to 1 for 
n = 0. Why do you think it should be 2?

Franklin T. Adams-Watters

-----Original Message-----
From: Andrew Weimholt <andrew.weimholt at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Mon, Feb 9, 2015 3:29 am
Subject: [seqfan] A027624 initial term


Hi,

I believe the first term of A027624 should be 2, not 1.

The history shows that Eric W. Weisstein was going to make such a
"correction" a while back, but then changed his mind and backed out the
change.

Can anyone offer an explanation?

Andrew

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From franktaw at netscape.net  Mon Feb  9 11:14:12 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Mon, 9 Feb 2015 05:14:12 -0500
Subject: [seqfan] Re: A027624 initial term
In-Reply-To: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>
References: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>
Message-ID: <8D21268490AA7E6-13DC-3722F@webmail-va003.sysops.aol.com>

Sorry, I typed the wrong sequence number. Please ignore my previous 
message.

Franklin T. Adams-Watters

-----Original Message-----
From: Andrew Weimholt <andrew.weimholt at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Mon, Feb 9, 2015 3:29 am
Subject: [seqfan] A027624 initial term


Hi,

I believe the first term of A027624 should be 2, not 1.

The history shows that Eric W. Weisstein was going to make such a
"correction" a while back, but then changed his mind and backed out the
change.

Can anyone offer an explanation?

Andrew

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From peter.luschny at gmail.com  Wed Feb 11 11:30:35 2015
From: peter.luschny at gmail.com (Peter Luschny)
Date: Wed, 11 Feb 2015 11:30:35 +0100
Subject: [seqfan] A marginal observation on some tables of R. H. Hardin
Message-ID: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>

In  A250544, A223069, A250669, A250692
R. H. Hardin gives the empirical recurrence

a(n) = 16*a(n-1)-106*a(n-2)+376*a(n-3)-769*a(n-4)
       +904*a(n-5)-564*a(n-6)+144*a(n-7)

I simply wish to observe that these coefficients are
listed in the ninth row of Peter Bala's A246117.

Peter


From seqfan at hasler.fr  Wed Feb 11 12:48:59 2015
From: seqfan at hasler.fr (M. F. Hasler)
Date: Wed, 11 Feb 2015 07:48:59 -0400
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
Message-ID: <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>

I added your comment in A250544, and also several missing
cross-references to sequences which list the rows/cols.
It would be nice if others could edit related sequences in a similar manner.

Maximilian

On Wed, Feb 11, 2015 at 6:30 AM, Peter Luschny <peter.luschny at gmail.com> wrote:
> In  A250544, A223069, A250669, A250692
> R. H. Hardin gives the empirical recurrence
>
> a(n) = 16*a(n-1)-106*a(n-2)+376*a(n-3)-769*a(n-4)
>        +904*a(n-5)-564*a(n-6)+144*a(n-7)
>
> I simply wish to observe that these coefficients are
> listed in the ninth row of Peter Bala's A246117.
>
> Peter


From rhhardin at att.net  Wed Feb 11 13:05:10 2015
From: rhhardin at att.net (Ron Hardin)
Date: Wed, 11 Feb 2015 04:05:10 -0800
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
Message-ID: <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>

The row/col/diag series always link to the table, so the refs link in the table will find them.

It always seemed like needless clutter to link the other way without a reason beyond existence.  It seems to claim significance beyond that.

The inbound links by contrast say that there are more like this, in this family.

 
rhhardin at mindspring.com
rhhardin at att.net (either)


>________________________________
> From: M. F. Hasler <seqfan at hasler.fr>
>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
>Sent: Wednesday, February 11, 2015 6:48 AM
>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
> 
>
>I added your comment in A250544, and also several missing
>cross-references to sequences which list the rows/cols.
>It would be nice if others could edit related sequences in a similar manner.
>
>Maximilian
>
>


From seqfan at hasler.fr  Wed Feb 11 13:23:03 2015
From: seqfan at hasler.fr (M. F. Hasler)
Date: Wed, 11 Feb 2015 08:23:03 -0400
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
Message-ID: <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>

Ron,

I am also personally against duplicating links (really never
understood why an A-number put somewhere in comment or formula should
be repeated in Xrefs), but it is nonetheless handy to have the links
to the column sequences because else you have to do a search with only
the sequence number in order to find them via the backlink, but often
you come there following a link and not doing a search (and it is
somehow counter-intuitive to copy-paste the number of the sequence
already displayed on the screen again into the search box...).

Also, in the present case there was no link to the tables A250676 and
A250691 with almost identical definition, and they would not pop up
doing a search for the other sequence numbers.

I also agree on the "significance" issue, and it is painfully to have
a bunch of sequence numbers in the Xrefs without knowing why they are
there. But with 2-3 words of explanation or just hints, this is a true
added value, I think.

Maximilian


On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
> The row/col/diag series always link to the table, so the refs link in the table will find them.
>
> It always seemed like needless clutter to link the other way without a reason beyond existence.  It seems to claim significance beyond that.
>
> The inbound links by contrast say that there are more like this, in this family.
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
>>________________________________
>> From: M. F. Hasler <seqfan at hasler.fr>
>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>Sent: Wednesday, February 11, 2015 6:48 AM
>>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>>
>>
>>I added your comment in A250544, and also several missing
>>cross-references to sequences which list the rows/cols.
>>It would be nice if others could edit related sequences in a similar manner.
>>
>>Maximilian
>>
>>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/


From rhhardin at att.net  Wed Feb 11 13:34:33 2015
From: rhhardin at att.net (Ron Hardin)
Date: Wed, 11 Feb 2015 04:34:33 -0800
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
Message-ID: <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>

I agree than any specific case can benefit from two-way links, but not in general.  At least it seems that way to me.


I don't understand the first paragraph problem you describe below.  Clicking "refs" in the header of the table gives you a nice page with all the rows and columns and diagonals expanded for you, as well as any foreign sequence that happens to reference inwards.

 
rhhardin at mindspring.com
rhhardin at att.net (either)


>________________________________
> From: M. F. Hasler <seqfan at hasler.fr>
>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
>Sent: Wednesday, February 11, 2015 7:23 AM
>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
> 
>
>Ron,
>
>I am also personally against duplicating links (really never
>understood why an A-number put somewhere in comment or formula should
>be repeated in Xrefs), but it is nonetheless handy to have the links
>to the column sequences because else you have to do a search with only
>the sequence number in order to find them via the backlink, but often
>you come there following a link and not doing a search (and it is
>somehow counter-intuitive to copy-paste the number of the sequence
>already displayed on the screen again into the search box...).
>
>Also, in the present case there was no link to the tables A250676 and
>A250691 with almost identical definition, and they would not pop up
>doing a search for the other sequence numbers.
>
>I also agree on the "significance" issue, and it is painfully to have
>a bunch of sequence numbers in the Xrefs without knowing why they are
>there. But with 2-3 words of explanation or just hints, this is a true
>added value, I think.
>
>Maximilian
>
>
>On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
>> The row/col/diag series always link to the table, so the refs link in the table will find them.
>>
>> It always seemed like needless clutter to link the other way without a reason beyond existence.  It seems to claim significance beyond that.
>>
>> The inbound links by contrast say that there are more like this, in this family.
>>
>>
>> rhhardin at mindspring.com
>> rhhardin at att.net (either)
>>
>>
>>>________________________________
>>> From: M. F. Hasler <seqfan at hasler.fr>
>>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>>Sent: Wednesday, February 11, 2015 6:48 AM
>>>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>>>
>>>
>>>I added your comment in A250544, and also several missing
>>>cross-references to sequences which list the rows/cols.
>>>It would be nice if others could edit related sequences in a similar manner.
>>>
>>>Maximilian
>>>
>>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>
>


From Eric.Angelini at kntv.be  Wed Feb 11 14:21:52 2015
From: Eric.Angelini at kntv.be (Eric Angelini)
Date: Wed, 11 Feb 2015 14:21:52 +0100
Subject: [seqfan] a(a(n)+a(n+1)) has property X
Message-ID: <8B00BFBA136BAB43AD27F9EDC3758F03BD24CA4FD9@KNTVSRV01.kntv.local>

Hello SeqFans,
S is the lexico-first permutation of the positive integers with the property ? a(a(n)+a(n+1)) is even ?

S = 1, 2, 4, 3, 5, 6, 8, 10, 7, 9, 12, 11, 13, 14, 15, 16, 18, 20, 17, 19, 22, 21, 24, 26, 23, 25, 28, 27, 30, 29, 32, 31, 33, 34, 35, 36, 38, 40, ...

In other words:
a)  take two adjacent integers x and y in S
b)  let (x + y) = z
c)  a(z) is even.
S was extended with the smallest integer not yet in S and not leading to a contradiction.

Testing the formula:
n = 1  2  3  4  5  6  7   8  9  10 11  12  13  14  15  16  17  18  19  20  21  22 ...
S = 1, 2, 4, 3, 5, 6, 8, 10, 7, 9, 12, 11, 13, 14, 15, 16, 18, 20, 17, 19, 22, 21,...

for n=1 then a(1)=1 and a(2)=2 and a(sum) reads a(1+2) reads a(3) which is 4 (even);
for n=2 then a(2)=2 and a(3)=4 and a(sum) reads a(2+4) reads a(6) which is 6 (even);
for n=3 then a(3)=4 and a(4)=3 and a(sum) reads a(4+3) reads a(7) which is 8 (even);
for n=4 then a(4)=3 and a(5)=5 and a(sum) reads a(3+5) reads a(8) which is 10 (even);
... etc.
--------------------------------------------------------------------
Remark #1:
The seq T, where a(a(n)+a(n+1)) is always odd is already in the OEIS:
https://oeis.org/A000027
;-D
But if we force a(1)=2 we then get again a permutation of A000027:

T' = 2, 1, 3, 5, 4, 6, 7, 9, 11, 13, 8, 10, 15, 12, ,14, 17, 16, 19, 18, 21, 23, 20, 22, 25, 27, 29, 31, 24, 26, 28, 33, ...

--------------------------------------------------------------------
Remark #2:
The seq P, where a(a(n)+a(n+1)) is always prime is also a permutation of of A000027:

P = 1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 13, 10, 17, 12, 19, 14, 15, 23, 29, 31, 16, 37, 41, 18, ...

Best,
?.







From njasloane at gmail.com  Wed Feb 11 17:23:16 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 11:23:16 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
Message-ID: <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>

Just to clarify one point:

The rule is that if there is a line anywhere in the entry that
mentions A123456, then Cf. A123456 should also appear in the
cross-references section.

(there are two good reasons: so Russ's code works
properly, and so the user can easily see if A123456 is
referred to anywhere in the entry without having to search through every
line)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net> wrote:

> I agree than any specific case can benefit from two-way links, but not in
> general.  At least it seems that way to me.
>
>
> I don't understand the first paragraph problem you describe below.
> Clicking "refs" in the header of the table gives you a nice page with all
> the rows and columns and diagonals expanded for you, as well as any foreign
> sequence that happens to reference inwards.
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
> >________________________________
> > From: M. F. Hasler <seqfan at hasler.fr>
> >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >Sent: Wednesday, February 11, 2015 7:23 AM
> >Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> Hardin
> >
> >
> >Ron,
> >
> >I am also personally against duplicating links (really never
> >understood why an A-number put somewhere in comment or formula should
> >be repeated in Xrefs), but it is nonetheless handy to have the links
> >to the column sequences because else you have to do a search with only
> >the sequence number in order to find them via the backlink, but often
> >you come there following a link and not doing a search (and it is
> >somehow counter-intuitive to copy-paste the number of the sequence
> >already displayed on the screen again into the search box...).
> >
> >Also, in the present case there was no link to the tables A250676 and
> >A250691 with almost identical definition, and they would not pop up
> >doing a search for the other sequence numbers.
> >
> >I also agree on the "significance" issue, and it is painfully to have
> >a bunch of sequence numbers in the Xrefs without knowing why they are
> >there. But with 2-3 words of explanation or just hints, this is a true
> >added value, I think.
> >
> >Maximilian
> >
> >
> >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
> >> The row/col/diag series always link to the table, so the refs link in
> the table will find them.
> >>
> >> It always seemed like needless clutter to link the other way without a
> reason beyond existence.  It seems to claim significance beyond that.
> >>
> >> The inbound links by contrast say that there are more like this, in
> this family.
> >>
> >>
> >> rhhardin at mindspring.com
> >> rhhardin at att.net (either)
> >>
> >>
> >>>________________________________
> >>> From: M. F. Hasler <seqfan at hasler.fr>
> >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >>>Sent: Wednesday, February 11, 2015 6:48 AM
> >>>Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> Hardin
> >>>
> >>>
> >>>I added your comment in A250544, and also several missing
> >>>cross-references to sequences which list the rows/cols.
> >>>It would be nice if others could edit related sequences in a similar
> manner.
> >>>
> >>>Maximilian
> >>>
> >>>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> >
> >
> >_______________________________________________
> >
> >Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From charles.greathouse at case.edu  Wed Feb 11 20:15:32 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Wed, 11 Feb 2015 14:15:32 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
Message-ID: <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>

What part of Russ' code work improperly when a sequence is in an entry but
not the xref field?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com> wrote:

> Just to clarify one point:
>
> The rule is that if there is a line anywhere in the entry that
> mentions A123456, then Cf. A123456 should also appear in the
> cross-references section.
>
> (there are two good reasons: so Russ's code works
> properly, and so the user can easily see if A123456 is
> referred to anywhere in the entry without having to search through every
> line)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net> wrote:
>
> > I agree than any specific case can benefit from two-way links, but not in
> > general.  At least it seems that way to me.
> >
> >
> > I don't understand the first paragraph problem you describe below.
> > Clicking "refs" in the header of the table gives you a nice page with all
> > the rows and columns and diagonals expanded for you, as well as any
> foreign
> > sequence that happens to reference inwards.
> >
> >
> > rhhardin at mindspring.com
> > rhhardin at att.net (either)
> >
> >
> > >________________________________
> > > From: M. F. Hasler <seqfan at hasler.fr>
> > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > >Sent: Wednesday, February 11, 2015 7:23 AM
> > >Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> > Hardin
> > >
> > >
> > >Ron,
> > >
> > >I am also personally against duplicating links (really never
> > >understood why an A-number put somewhere in comment or formula should
> > >be repeated in Xrefs), but it is nonetheless handy to have the links
> > >to the column sequences because else you have to do a search with only
> > >the sequence number in order to find them via the backlink, but often
> > >you come there following a link and not doing a search (and it is
> > >somehow counter-intuitive to copy-paste the number of the sequence
> > >already displayed on the screen again into the search box...).
> > >
> > >Also, in the present case there was no link to the tables A250676 and
> > >A250691 with almost identical definition, and they would not pop up
> > >doing a search for the other sequence numbers.
> > >
> > >I also agree on the "significance" issue, and it is painfully to have
> > >a bunch of sequence numbers in the Xrefs without knowing why they are
> > >there. But with 2-3 words of explanation or just hints, this is a true
> > >added value, I think.
> > >
> > >Maximilian
> > >
> > >
> > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
> > >> The row/col/diag series always link to the table, so the refs link in
> > the table will find them.
> > >>
> > >> It always seemed like needless clutter to link the other way without a
> > reason beyond existence.  It seems to claim significance beyond that.
> > >>
> > >> The inbound links by contrast say that there are more like this, in
> > this family.
> > >>
> > >>
> > >> rhhardin at mindspring.com
> > >> rhhardin at att.net (either)
> > >>
> > >>
> > >>>________________________________
> > >>> From: M. F. Hasler <seqfan at hasler.fr>
> > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > >>>Sent: Wednesday, February 11, 2015 6:48 AM
> > >>>Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> > Hardin
> > >>>
> > >>>
> > >>>I added your comment in A250544, and also several missing
> > >>>cross-references to sequences which list the rows/cols.
> > >>>It would be nice if others could edit related sequences in a similar
> > manner.
> > >>>
> > >>>Maximilian
> > >>>
> > >>>
> > >>
> > >> _______________________________________________
> > >>
> > >> Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> > >
> > >
> > >
> > >_______________________________________________
> > >
> > >Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Wed Feb 11 20:41:00 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 14:41:00 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
Message-ID: <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>

 I forget.  But the main reason is for humans to be able to see at a glance
what sequences are mentioned.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> What part of Russ' code work improperly when a sequence is in an entry but
> not the xref field?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > Just to clarify one point:
> >
> > The rule is that if there is a line anywhere in the entry that
> > mentions A123456, then Cf. A123456 should also appear in the
> > cross-references section.
> >
> > (there are two good reasons: so Russ's code works
> > properly, and so the user can easily see if A123456 is
> > referred to anywhere in the entry without having to search through every
> > line)
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net> wrote:
> >
> > > I agree than any specific case can benefit from two-way links, but not
> in
> > > general.  At least it seems that way to me.
> > >
> > >
> > > I don't understand the first paragraph problem you describe below.
> > > Clicking "refs" in the header of the table gives you a nice page with
> all
> > > the rows and columns and diagonals expanded for you, as well as any
> > foreign
> > > sequence that happens to reference inwards.
> > >
> > >
> > > rhhardin at mindspring.com
> > > rhhardin at att.net (either)
> > >
> > >
> > > >________________________________
> > > > From: M. F. Hasler <seqfan at hasler.fr>
> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >Sent: Wednesday, February 11, 2015 7:23 AM
> > > >Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> > > Hardin
> > > >
> > > >
> > > >Ron,
> > > >
> > > >I am also personally against duplicating links (really never
> > > >understood why an A-number put somewhere in comment or formula should
> > > >be repeated in Xrefs), but it is nonetheless handy to have the links
> > > >to the column sequences because else you have to do a search with only
> > > >the sequence number in order to find them via the backlink, but often
> > > >you come there following a link and not doing a search (and it is
> > > >somehow counter-intuitive to copy-paste the number of the sequence
> > > >already displayed on the screen again into the search box...).
> > > >
> > > >Also, in the present case there was no link to the tables A250676 and
> > > >A250691 with almost identical definition, and they would not pop up
> > > >doing a search for the other sequence numbers.
> > > >
> > > >I also agree on the "significance" issue, and it is painfully to have
> > > >a bunch of sequence numbers in the Xrefs without knowing why they are
> > > >there. But with 2-3 words of explanation or just hints, this is a true
> > > >added value, I think.
> > > >
> > > >Maximilian
> > > >
> > > >
> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
> > > >> The row/col/diag series always link to the table, so the refs link
> in
> > > the table will find them.
> > > >>
> > > >> It always seemed like needless clutter to link the other way
> without a
> > > reason beyond existence.  It seems to claim significance beyond that.
> > > >>
> > > >> The inbound links by contrast say that there are more like this, in
> > > this family.
> > > >>
> > > >>
> > > >> rhhardin at mindspring.com
> > > >> rhhardin at att.net (either)
> > > >>
> > > >>
> > > >>>________________________________
> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> > > Hardin
> > > >>>
> > > >>>
> > > >>>I added your comment in A250544, and also several missing
> > > >>>cross-references to sequences which list the rows/cols.
> > > >>>It would be nice if others could edit related sequences in a similar
> > > manner.
> > > >>>
> > > >>>Maximilian
> > > >>>
> > > >>>
> > > >>
> > > >> _______________________________________________
> > > >>
> > > >> Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >_______________________________________________
> > > >
> > > >Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > > >
> > > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From franktaw at netscape.net  Wed Feb 11 20:56:01 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Wed, 11 Feb 2015 14:56:01 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
Message-ID: <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>

Just as a point of reference, a search for "A000217 -xref:A000217" 
gives 933 matches, out of 2699 that match "A000217".

Franklin T. Adams-Watters

-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Wed, Feb 11, 2015 1:41 pm
Subject: [seqfan] Re: A marginal observation on some tables of R. H. 
Hardin


  I forget.  But the main reason is for humans to be able to see at a 
glance
what sequences are mentioned.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> What part of Russ' code work improperly when a sequence is in an 
entry but
> not the xref field?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com> 
wrote:
>
> > Just to clarify one point:
> >
> > The rule is that if there is a line anywhere in the entry that
> > mentions A123456, then Cf. A123456 should also appear in the
> > cross-references section.
> >
> > (there are two good reasons: so Russ's code works
> > properly, and so the user can easily see if A123456 is
> > referred to anywhere in the entry without having to search through 
every
> > line)
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, 
Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net> 
wrote:
> >
> > > I agree than any specific case can benefit from two-way links, 
but not
> in
> > > general.  At least it seems that way to me.
> > >
> > >
> > > I don't understand the first paragraph problem you describe below.
> > > Clicking "refs" in the header of the table gives you a nice page 
with
> all
> > > the rows and columns and diagonals expanded for you, as well as 
any
> > foreign
> > > sequence that happens to reference inwards.
> > >
> > >
> > > rhhardin at mindspring.com
> > > rhhardin at att.net (either)
> > >
> > >
> > > >________________________________
> > > > From: M. F. Hasler <seqfan at hasler.fr>
> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >Sent: Wednesday, February 11, 2015 7:23 AM
> > > >Subject: [seqfan] Re: A marginal observation on some tables of 
R. H.
> > > Hardin
> > > >
> > > >
> > > >Ron,
> > > >
> > > >I am also personally against duplicating links (really never
> > > >understood why an A-number put somewhere in comment or formula 
should
> > > >be repeated in Xrefs), but it is nonetheless handy to have the 
links
> > > >to the column sequences because else you have to do a search 
with only
> > > >the sequence number in order to find them via the backlink, but 
often
> > > >you come there following a link and not doing a search (and it is
> > > >somehow counter-intuitive to copy-paste the number of the 
sequence
> > > >already displayed on the screen again into the search box...).
> > > >
> > > >Also, in the present case there was no link to the tables 
A250676 and
> > > >A250691 with almost identical definition, and they would not pop 
up
> > > >doing a search for the other sequence numbers.
> > > >
> > > >I also agree on the "significance" issue, and it is painfully to 
have
> > > >a bunch of sequence numbers in the Xrefs without knowing why 
they are
> > > >there. But with 2-3 words of explanation or just hints, this is 
a true
> > > >added value, I think.
> > > >
> > > >Maximilian
> > > >
> > > >
> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> 
wrote:
> > > >> The row/col/diag series always link to the table, so the refs 
link
> in
> > > the table will find them.
> > > >>
> > > >> It always seemed like needless clutter to link the other way
> without a
> > > reason beyond existence.  It seems to claim significance beyond 
that.
> > > >>
> > > >> The inbound links by contrast say that there are more like 
this, in
> > > this family.
> > > >>
> > > >>
> > > >> rhhardin at mindspring.com
> > > >> rhhardin at att.net (either)
> > > >>
> > > >>
> > > >>>________________________________
> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of 
R. H.
> > > Hardin
> > > >>>
> > > >>>
> > > >>>I added your comment in A250544, and also several missing
> > > >>>cross-references to sequences which list the rows/cols.
> > > >>>It would be nice if others could edit related sequences in a 
similar
> > > manner.
> > > >>>
> > > >>>Maximilian
> > > >>>
> > > >>>
> > > >>
> > > >> _______________________________________________
> > > >>
> > > >> Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >_______________________________________________
> > > >
> > > >Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > > >
> > > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From peter.luschny at gmail.com  Wed Feb 11 21:30:20 2015
From: peter.luschny at gmail.com (Peter Luschny)
Date: Wed, 11 Feb 2015 21:30:20 +0100
Subject: [seqfan]  A marginal observation on some tables of R. H. Hardin
Message-ID: <CAMMbGZbB6H5OtU6jTzwNemCWg19bvv76aCr77TqEjMsxuQBHDw@mail.gmail.com>

The discussion went slightly off-topic, and the old habit
to change the name of a thread when the topic changes
seems to be a forgotten virtue.

But let me come back to Hardin's empirical recurrence.

I do not think that it is a coincidence that the coefficients
appear in Bala's A246117 although this is hard demonstrate
at the moment.

In the spirit of experimental math let me look also at
the recurrences a(n) and b(n) (case 2 and 3 in a more
general setup which makes Hardin's c(n) the case 4).

a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3),
b(n) = 9*b(n-1)-31*b(n-2)+51*b(n-3)-40*b(n-4)+12*b(n-5),
c(n) = 16*c(n-1)-106*c(n-2)+376*c(n-3)-769*c(n-4)+904*c(n-5)-564*c(n-6)+144*c(n-7).

So now my problem are meaningful initial terms,
a(0), a(1), a(2) and b(0), b(1), b(2), b(3), b(4).

Any suggestions for the initial terms?

Peter


From njasloane at gmail.com  Wed Feb 11 21:35:03 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 15:35:03 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
Message-ID: <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>

I cannot understand why there is ever an objection to
cross-references.

If you are using the OEIS for
what it chiefly intended for, its main purpose, which is to help
you (very often, me) understand a sequence that has come
up in your work, then any hint at all is potentially valuable.

A cross-reference is like someone whispering to you, "I don't know if it
will help, but did you look at A...... ? "

And they should all be listed in the cross-reference section,
so it is easy to find them.



Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> Just as a point of reference, a search for "A000217 -xref:A000217" gives
> 933 matches, out of 2699 that match "A000217".
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Neil Sloane <njasloane at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Feb 11, 2015 1:41 pm
> Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>
>
>  I forget.  But the main reason is for humans to be able to see at a glance
> what sequences are mentioned.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>  What part of Russ' code work improperly when a sequence is in an
>>
> entry but
>
>> not the xref field?
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
>>
> wrote:
>
>>
>> > Just to clarify one point:
>> >
>> > The rule is that if there is a line anywhere in the entry that
>> > mentions A123456, then Cf. A123456 should also appear in the
>> > cross-references section.
>> >
>> > (there are two good reasons: so Russ's code works
>> > properly, and so the user can easily see if A123456 is
>> > referred to anywhere in the entry without having to search through
>>
> every
>
>> > line)
>> >
>> > Best regards
>> > Neil
>> >
>> > Neil J. A. Sloane, President, OEIS Foundation.
>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>>
> Piscataway, NJ.
>
>> > Phone: 732 828 6098; home page: http://NeilSloane.com
>> > Email: njasloane at gmail.com
>> >
>> >
>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
>>
> wrote:
>
>> >
>> > > I agree than any specific case can benefit from two-way links,
>>
> but not
>
>> in
>> > > general.  At least it seems that way to me.
>> > >
>> > >
>> > > I don't understand the first paragraph problem you describe below.
>> > > Clicking "refs" in the header of the table gives you a nice page
>>
> with
>
>> all
>> > > the rows and columns and diagonals expanded for you, as well as
>>
> any
>
>> > foreign
>> > > sequence that happens to reference inwards.
>> > >
>> > >
>> > > rhhardin at mindspring.com
>> > > rhhardin at att.net (either)
>> > >
>> > >
>> > > >________________________________
>> > > > From: M. F. Hasler <seqfan at hasler.fr>
>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
>>
> R. H.
>
>> > > Hardin
>> > > >
>> > > >
>> > > >Ron,
>> > > >
>> > > >I am also personally against duplicating links (really never
>> > > >understood why an A-number put somewhere in comment or formula
>>
> should
>
>> > > >be repeated in Xrefs), but it is nonetheless handy to have the
>>
> links
>
>> > > >to the column sequences because else you have to do a search
>>
> with only
>
>> > > >the sequence number in order to find them via the backlink, but
>>
> often
>
>> > > >you come there following a link and not doing a search (and it is
>> > > >somehow counter-intuitive to copy-paste the number of the
>>
> sequence
>
>> > > >already displayed on the screen again into the search box...).
>> > > >
>> > > >Also, in the present case there was no link to the tables
>>
> A250676 and
>
>> > > >A250691 with almost identical definition, and they would not pop
>>
> up
>
>> > > >doing a search for the other sequence numbers.
>> > > >
>> > > >I also agree on the "significance" issue, and it is painfully to
>>
> have
>
>> > > >a bunch of sequence numbers in the Xrefs without knowing why
>>
> they are
>
>> > > >there. But with 2-3 words of explanation or just hints, this is
>>
> a true
>
>> > > >added value, I think.
>> > > >
>> > > >Maximilian
>> > > >
>> > > >
>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
>>
> wrote:
>
>> > > >> The row/col/diag series always link to the table, so the refs
>>
> link
>
>> in
>> > > the table will find them.
>> > > >>
>> > > >> It always seemed like needless clutter to link the other way
>> without a
>> > > reason beyond existence.  It seems to claim significance beyond
>>
> that.
>
>> > > >>
>> > > >> The inbound links by contrast say that there are more like
>>
> this, in
>
>> > > this family.
>> > > >>
>> > > >>
>> > > >> rhhardin at mindspring.com
>> > > >> rhhardin at att.net (either)
>> > > >>
>> > > >>
>> > > >>>________________________________
>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
>>
> R. H.
>
>> > > Hardin
>> > > >>>
>> > > >>>
>> > > >>>I added your comment in A250544, and also several missing
>> > > >>>cross-references to sequences which list the rows/cols.
>> > > >>>It would be nice if others could edit related sequences in a
>>
> similar
>
>> > > manner.
>> > > >>>
>> > > >>>Maximilian
>> > > >>>
>> > > >>>
>> > > >>
>> > > >> _______________________________________________
>> > > >>
>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
>> > > >
>> > > >
>> > > >
>> > > >
>> > > >
>> > > >_______________________________________________
>> > > >
>> > > >Seqfan Mailing list - http://list.seqfan.eu/
>> > > >
>> > > >
>> > > >
>> > >
>> > > _______________________________________________
>> > >
>> > > Seqfan Mailing list - http://list.seqfan.eu/
>> > >
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From franktaw at netscape.net  Wed Feb 11 22:33:49 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Wed, 11 Feb 2015 16:33:49 -0500
Subject: [seqfan] Cross-refs (retitled)
In-Reply-To: <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
Message-ID: <8D214598E88EBBC-B34-43019@webmail-vm109.sysops.aol.com>

I'm not disagreeing with that. I'm just pointing out how far we are 
 from doing it that way. I did at one point do some searches for "base" 
sequences that did not have the keyword, and corrected a few hundred of 
them. I'm not going to do something similar for the thousands of 
exceptions to this rule.

I guess the first step is for the editors to start uniformly enforcing 
the rule for both new and modified sequences.

Actually, I do object to cross-refs that, if all references of this 
sort were added, thousands of cross-refs would be added to a single 
sequence. Consider, for the moment, the effect of adding a cross-ref 
 from A000040 to every sequence that mentions primes. Hints are good, 
but not when you can't see the trees for the forest.

Franklin T. Adams-Watters

-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Wed, Feb 11, 2015 2:35 pm
Subject: [seqfan] Re: A marginal observation on some tables of R. H. 
Hardin


I cannot understand why there is ever an objection to
cross-references.

If you are using the OEIS for
what it chiefly intended for, its main purpose, which is to help
you (very often, me) understand a sequence that has come
up in your work, then any hint at all is potentially valuable.

A cross-reference is like someone whispering to you, "I don't know if it
will help, but did you look at A...... ? "

And they should all be listed in the cross-reference section,
so it is easy to find them.



Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters 
<franktaw at netscape.net>
wrote:

> Just as a point of reference, a search for "A000217 -xref:A000217" 
gives
> 933 matches, out of 2699 that match "A000217".
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Neil Sloane <njasloane at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Feb 11, 2015 1:41 pm
> Subject: [seqfan] Re: A marginal observation on some tables of R. H. 
Hardin
>
>
>  I forget.  But the main reason is for humans to be able to see at a 
glance
> what sequences are mentioned.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>  What part of Russ' code work improperly when a sequence is in an
>>
> entry but
>
>> not the xref field?
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
>>
> wrote:
>
>>
>> > Just to clarify one point:
>> >
>> > The rule is that if there is a line anywhere in the entry that
>> > mentions A123456, then Cf. A123456 should also appear in the
>> > cross-references section.
>> >
>> > (there are two good reasons: so Russ's code works
>> > properly, and so the user can easily see if A123456 is
>> > referred to anywhere in the entry without having to search through
>>
> every
>
>> > line)
>> >
>> > Best regards
>> > Neil
>> >
>> > Neil J. A. Sloane, President, OEIS Foundation.
>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>>
> Piscataway, NJ.
>
>> > Phone: 732 828 6098; home page: http://NeilSloane.com
>> > Email: njasloane at gmail.com
>> >
>> >
>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
>>
> wrote:
>
>> >
>> > > I agree than any specific case can benefit from two-way links,
>>
> but not
>
>> in
>> > > general.  At least it seems that way to me.
>> > >
>> > >
>> > > I don't understand the first paragraph problem you describe 
below.
>> > > Clicking "refs" in the header of the table gives you a nice page
>>
> with
>
>> all
>> > > the rows and columns and diagonals expanded for you, as well as
>>
> any
>
>> > foreign
>> > > sequence that happens to reference inwards.
>> > >
>> > >
>> > > rhhardin at mindspring.com
>> > > rhhardin at att.net (either)
>> > >
>> > >
>> > > >________________________________
>> > > > From: M. F. Hasler <seqfan at hasler.fr>
>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
>>
> R. H.
>
>> > > Hardin
>> > > >
>> > > >
>> > > >Ron,
>> > > >
>> > > >I am also personally against duplicating links (really never
>> > > >understood why an A-number put somewhere in comment or formula
>>
> should
>
>> > > >be repeated in Xrefs), but it is nonetheless handy to have the
>>
> links
>
>> > > >to the column sequences because else you have to do a search
>>
> with only
>
>> > > >the sequence number in order to find them via the backlink, but
>>
> often
>
>> > > >you come there following a link and not doing a search (and it 
is
>> > > >somehow counter-intuitive to copy-paste the number of the
>>
> sequence
>
>> > > >already displayed on the screen again into the search box...).
>> > > >
>> > > >Also, in the present case there was no link to the tables
>>
> A250676 and
>
>> > > >A250691 with almost identical definition, and they would not pop
>>
> up
>
>> > > >doing a search for the other sequence numbers.
>> > > >
>> > > >I also agree on the "significance" issue, and it is painfully to
>>
> have
>
>> > > >a bunch of sequence numbers in the Xrefs without knowing why
>>
> they are
>
>> > > >there. But with 2-3 words of explanation or just hints, this is
>>
> a true
>
>> > > >added value, I think.
>> > > >
>> > > >Maximilian
>> > > >
>> > > >
>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
>>
> wrote:
>
>> > > >> The row/col/diag series always link to the table, so the refs
>>
> link
>
>> in
>> > > the table will find them.
>> > > >>
>> > > >> It always seemed like needless clutter to link the other way
>> without a
>> > > reason beyond existence.  It seems to claim significance beyond
>>
> that.
>
>> > > >>
>> > > >> The inbound links by contrast say that there are more like
>>
> this, in
>
>> > > this family.
>> > > >>
>> > > >>
>> > > >> rhhardin at mindspring.com
>> > > >> rhhardin at att.net (either)
>> > > >>
>> > > >>
>> > > >>>________________________________
>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
>>
> R. H.
>
>> > > Hardin
>> > > >>>
>> > > >>>
>> > > >>>I added your comment in A250544, and also several missing
>> > > >>>cross-references to sequences which list the rows/cols.
>> > > >>>It would be nice if others could edit related sequences in a
>>
> similar
>
>> > > manner.
>> > > >>>
>> > > >>>Maximilian
>> > > >>>
>> > > >>>
>> > > >>
>> > > >> _______________________________________________
>> > > >>
>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
>> > > >
>> > > >
>> > > >
>> > > >
>> > > >
>> > > >_______________________________________________
>> > > >
>> > > >Seqfan Mailing list - http://list.seqfan.eu/
>> > > >
>> > > >
>> > > >
>> > >
>> > > _______________________________________________
>> > >
>> > > Seqfan Mailing list - http://list.seqfan.eu/
>> > >
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From njasloane at gmail.com  Wed Feb 11 22:54:50 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 16:54:50 -0500
Subject: [seqfan] Re: Cross-refs (retitled)
In-Reply-To: <8D214598E88EBBC-B34-43019@webmail-vm109.sysops.aol.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
 <8D214598E88EBBC-B34-43019@webmail-vm109.sysops.aol.com>
Message-ID: <CAAOnSgQwmzTMTk9WKQc0USfOFuMR6Z8Jy3G98yJQ=P7=Vb6+pg@mail.gmail.com>

I certainly was not suggesting that if A references B then B should
reference A.  That has never been a rule.

(There are remarks about this in one of the ancient
"format of entries" files.)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 4:33 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> I'm not disagreeing with that. I'm just pointing out how far we are from
> doing it that way. I did at one point do some searches for "base" sequences
> that did not have the keyword, and corrected a few hundred of them. I'm not
> going to do something similar for the thousands of exceptions to this rule.
>
> I guess the first step is for the editors to start uniformly enforcing the
> rule for both new and modified sequences.
>
> Actually, I do object to cross-refs that, if all references of this sort
> were added, thousands of cross-refs would be added to a single sequence.
> Consider, for the moment, the effect of adding a cross-ref from A000040 to
> every sequence that mentions primes. Hints are good, but not when you can't
> see the trees for the forest.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Neil Sloane <njasloane at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Feb 11, 2015 2:35 pm
> Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>
>
> I cannot understand why there is ever an objection to
> cross-references.
>
> If you are using the OEIS for
> what it chiefly intended for, its main purpose, which is to help
> you (very often, me) understand a sequence that has come
> up in your work, then any hint at all is potentially valuable.
>
> A cross-reference is like someone whispering to you, "I don't know if it
> will help, but did you look at A...... ? "
>
> And they should all be listed in the cross-reference section,
> so it is easy to find them.
>
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters <
> franktaw at netscape.net>
> wrote:
>
>  Just as a point of reference, a search for "A000217 -xref:A000217"
>>
> gives
>
>> 933 matches, out of 2699 that match "A000217".
>>
>> Franklin T. Adams-Watters
>>
>> -----Original Message-----
>> From: Neil Sloane <njasloane at gmail.com>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Wed, Feb 11, 2015 1:41 pm
>> Subject: [seqfan] Re: A marginal observation on some tables of R. H.
>>
> Hardin
>
>>
>>
>>  I forget.  But the main reason is for humans to be able to see at a
>>
> glance
>
>> what sequences are mentioned.
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
>>
> NJ.
>
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
>> charles.greathouse at case.edu> wrote:
>>
>>  What part of Russ' code work improperly when a sequence is in an
>>
>>>
>>>  entry but
>>
>>  not the xref field?
>>>
>>> Charles Greathouse
>>> Analyst/Programmer
>>> Case Western Reserve University
>>>
>>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
>>>
>>>  wrote:
>>
>>
>>> > Just to clarify one point:
>>> >
>>> > The rule is that if there is a line anywhere in the entry that
>>> > mentions A123456, then Cf. A123456 should also appear in the
>>> > cross-references section.
>>> >
>>> > (there are two good reasons: so Russ's code works
>>> > properly, and so the user can easily see if A123456 is
>>> > referred to anywhere in the entry without having to search through
>>>
>>>  every
>>
>>  > line)
>>> >
>>> > Best regards
>>> > Neil
>>> >
>>> > Neil J. A. Sloane, President, OEIS Foundation.
>>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>>>
>>>  Piscataway, NJ.
>>
>>  > Phone: 732 828 6098; home page: http://NeilSloane.com
>>> > Email: njasloane at gmail.com
>>> >
>>> >
>>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
>>>
>>>  wrote:
>>
>>  >
>>> > > I agree than any specific case can benefit from two-way links,
>>>
>>>  but not
>>
>>  in
>>> > > general.  At least it seems that way to me.
>>> > >
>>> > >
>>> > > I don't understand the first paragraph problem you describe
>>>
>> below.
>
>> > > Clicking "refs" in the header of the table gives you a nice page
>>>
>>>  with
>>
>>  all
>>> > > the rows and columns and diagonals expanded for you, as well as
>>>
>>>  any
>>
>>  > foreign
>>> > > sequence that happens to reference inwards.
>>> > >
>>> > >
>>> > > rhhardin at mindspring.com
>>> > > rhhardin at att.net (either)
>>> > >
>>> > >
>>> > > >________________________________
>>> > > > From: M. F. Hasler <seqfan at hasler.fr>
>>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
>>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
>>>
>>>  R. H.
>>
>>  > > Hardin
>>> > > >
>>> > > >
>>> > > >Ron,
>>> > > >
>>> > > >I am also personally against duplicating links (really never
>>> > > >understood why an A-number put somewhere in comment or formula
>>>
>>>  should
>>
>>  > > >be repeated in Xrefs), but it is nonetheless handy to have the
>>>
>>>  links
>>
>>  > > >to the column sequences because else you have to do a search
>>>
>>>  with only
>>
>>  > > >the sequence number in order to find them via the backlink, but
>>>
>>>  often
>>
>>  > > >you come there following a link and not doing a search (and it
>>>
>> is
>
>> > > >somehow counter-intuitive to copy-paste the number of the
>>>
>>>  sequence
>>
>>  > > >already displayed on the screen again into the search box...).
>>> > > >
>>> > > >Also, in the present case there was no link to the tables
>>>
>>>  A250676 and
>>
>>  > > >A250691 with almost identical definition, and they would not pop
>>>
>>>  up
>>
>>  > > >doing a search for the other sequence numbers.
>>> > > >
>>> > > >I also agree on the "significance" issue, and it is painfully to
>>>
>>>  have
>>
>>  > > >a bunch of sequence numbers in the Xrefs without knowing why
>>>
>>>  they are
>>
>>  > > >there. But with 2-3 words of explanation or just hints, this is
>>>
>>>  a true
>>
>>  > > >added value, I think.
>>> > > >
>>> > > >Maximilian
>>> > > >
>>> > > >
>>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
>>>
>>>  wrote:
>>
>>  > > >> The row/col/diag series always link to the table, so the refs
>>>
>>>  link
>>
>>  in
>>> > > the table will find them.
>>> > > >>
>>> > > >> It always seemed like needless clutter to link the other way
>>> without a
>>> > > reason beyond existence.  It seems to claim significance beyond
>>>
>>>  that.
>>
>>  > > >>
>>> > > >> The inbound links by contrast say that there are more like
>>>
>>>  this, in
>>
>>  > > this family.
>>> > > >>
>>> > > >>
>>> > > >> rhhardin at mindspring.com
>>> > > >> rhhardin at att.net (either)
>>> > > >>
>>> > > >>
>>> > > >>>________________________________
>>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
>>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
>>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
>>>
>>>  R. H.
>>
>>  > > Hardin
>>> > > >>>
>>> > > >>>
>>> > > >>>I added your comment in A250544, and also several missing
>>> > > >>>cross-references to sequences which list the rows/cols.
>>> > > >>>It would be nice if others could edit related sequences in a
>>>
>>>  similar
>>
>>  > > manner.
>>> > > >>>
>>> > > >>>Maximilian
>>> > > >>>
>>> > > >>>
>>> > > >>
>>> > > >> _______________________________________________
>>> > > >>
>>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
>>> > > >
>>> > > >
>>> > > >
>>> > > >
>>> > > >
>>> > > >_______________________________________________
>>> > > >
>>> > > >Seqfan Mailing list - http://list.seqfan.eu/
>>> > > >
>>> > > >
>>> > > >
>>> > >
>>> > > _______________________________________________
>>> > >
>>> > > Seqfan Mailing list - http://list.seqfan.eu/
>>> > >
>>> >
>>> > _______________________________________________
>>> >
>>> > Seqfan Mailing list - http://list.seqfan.eu/
>>> >
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>>>  _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From rhhardin at att.net  Wed Feb 11 23:05:57 2015
From: rhhardin at att.net (Ron Hardin)
Date: Wed, 11 Feb 2015 14:05:57 -0800
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
Message-ID: <1423692357.25896.YahooMailNeo@web185002.mail.gq1.yahoo.com>

It's easy to add the %Y lines (done!) to the generating programs but it changes how you look at the line if it's an index of mentions above rather than something you might want to look at as decided by a human.  Either way is okay.  It just changes the use.

The count-against is that you lose the human editor, and so may skip them all because so many are useless.

 
rhhardin at mindspring.com
rhhardin at att.net (either)


>________________________________
> From: Neil Sloane <njasloane at gmail.com>
>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
>Sent: Wednesday, February 11, 2015 3:35 PM
>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
> 
>
>I cannot understand why there is ever an objection to
>cross-references.
>
>If you are using the OEIS for
>what it chiefly intended for, its main purpose, which is to help
>you (very often, me) understand a sequence that has come
>up in your work, then any hint at all is potentially valuable.
>
>A cross-reference is like someone whispering to you, "I don't know if it
>will help, but did you look at A...... ? "
>
>And they should all be listed in the cross-reference section,
>so it is easy to find them.
>
>
>
>Best regards
>Neil
>
>Neil J. A. Sloane, President, OEIS Foundation.
>11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>Phone: 732 828 6098; home page: http://NeilSloane.com
>Email: njasloane at gmail.com
>
>
>On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters <franktaw at netscape.net>
>wrote:
>
>> Just as a point of reference, a search for "A000217 -xref:A000217" gives
>> 933 matches, out of 2699 that match "A000217".
>>
>> Franklin T. Adams-Watters
>>
>> -----Original Message-----
>> From: Neil Sloane <njasloane at gmail.com>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Wed, Feb 11, 2015 1:41 pm
>> Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>>
>>
>>  I forget.  But the main reason is for humans to be able to see at a glance
>> what sequences are mentioned.
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
>> charles.greathouse at case.edu> wrote:
>>
>>  What part of Russ' code work improperly when a sequence is in an
>>>
>> entry but
>>
>>> not the xref field?
>>>
>>> Charles Greathouse
>>> Analyst/Programmer
>>> Case Western Reserve University
>>>
>>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
>>>
>> wrote:
>>
>>>
>>> > Just to clarify one point:
>>> >
>>> > The rule is that if there is a line anywhere in the entry that
>>> > mentions A123456, then Cf. A123456 should also appear in the
>>> > cross-references section.
>>> >
>>> > (there are two good reasons: so Russ's code works
>>> > properly, and so the user can easily see if A123456 is
>>> > referred to anywhere in the entry without having to search through
>>>
>> every
>>
>>> > line)
>>> >
>>> > Best regards
>>> > Neil
>>> >
>>> > Neil J. A. Sloane, President, OEIS Foundation.
>>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>>>
>> Piscataway, NJ.
>>
>>> > Phone: 732 828 6098; home page: http://NeilSloane.com
>>> > Email: njasloane at gmail.com
>>> >
>>> >
>>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
>>>
>> wrote:
>>
>>> >
>>> > > I agree than any specific case can benefit from two-way links,
>>>
>> but not
>>
>>> in
>>> > > general.  At least it seems that way to me.
>>> > >
>>> > >
>>> > > I don't understand the first paragraph problem you describe below.
>>> > > Clicking "refs" in the header of the table gives you a nice page
>>>
>> with
>>
>>> all
>>> > > the rows and columns and diagonals expanded for you, as well as
>>>
>> any
>>
>>> > foreign
>>> > > sequence that happens to reference inwards.
>>> > >
>>> > >
>>> > > rhhardin at mindspring.com
>>> > > rhhardin at att.net (either)
>>> > >
>>> > >
>>> > > >________________________________
>>> > > > From: M. F. Hasler <seqfan at hasler.fr>
>>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
>>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
>>>
>> R. H.
>>
>>> > > Hardin
>>> > > >
>>> > > >
>>> > > >Ron,
>>> > > >
>>> > > >I am also personally against duplicating links (really never
>>> > > >understood why an A-number put somewhere in comment or formula
>>>
>> should
>>
>>> > > >be repeated in Xrefs), but it is nonetheless handy to have the
>>>
>> links
>>
>>> > > >to the column sequences because else you have to do a search
>>>
>> with only
>>
>>> > > >the sequence number in order to find them via the backlink, but
>>>
>> often
>>
>>> > > >you come there following a link and not doing a search (and it is
>>> > > >somehow counter-intuitive to copy-paste the number of the
>>>
>> sequence
>>
>>> > > >already displayed on the screen again into the search box...).
>>> > > >
>>> > > >Also, in the present case there was no link to the tables
>>>
>> A250676 and
>>
>>> > > >A250691 with almost identical definition, and they would not pop
>>>
>> up
>>
>>> > > >doing a search for the other sequence numbers.
>>> > > >
>>> > > >I also agree on the "significance" issue, and it is painfully to
>>>
>> have
>>
>>> > > >a bunch of sequence numbers in the Xrefs without knowing why
>>>
>> they are
>>
>>> > > >there. But with 2-3 words of explanation or just hints, this is
>>>
>> a true
>>
>>> > > >added value, I think.
>>> > > >
>>> > > >Maximilian
>>> > > >
>>> > > >
>>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
>>>
>> wrote:
>>
>>> > > >> The row/col/diag series always link to the table, so the refs
>>>
>> link
>>
>>> in
>>> > > the table will find them.
>>> > > >>
>>> > > >> It always seemed like needless clutter to link the other way
>>> without a
>>> > > reason beyond existence.  It seems to claim significance beyond
>>>
>> that.
>>
>>> > > >>
>>> > > >> The inbound links by contrast say that there are more like
>>>
>> this, in
>>
>>> > > this family.
>>> > > >>
>>> > > >>
>>> > > >> rhhardin at mindspring.com
>>> > > >> rhhardin at att.net (either)
>>> > > >>
>>> > > >>
>>> > > >>>________________________________
>>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
>>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
>>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
>>>
>> R. H.
>>
>>> > > Hardin
>>> > > >>>
>>> > > >>>
>>> > > >>>I added your comment in A250544, and also several missing
>>> > > >>>cross-references to sequences which list the rows/cols.
>>> > > >>>It would be nice if others could edit related sequences in a
>>>
>> similar
>>
>>> > > manner.
>>> > > >>>
>>> > > >>>Maximilian
>>> > > >>>
>>> > > >>>
>>> > > >>
>>> > > >> _______________________________________________
>>> > > >>
>>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>>> > > >
>>> > > >
>>> > > >
>>> > > >
>>> > > >
>>> > > >_______________________________________________
>>> > > >
>>> > > >Seqfan Mailing list - http://list.seqfan.eu/
>>> > > >
>>> > > >
>>> > > >
>>> > >
>>> > > _______________________________________________
>>> > >
>>> > > Seqfan Mailing list - http://list.seqfan.eu/
>>> > >
>>> >
>>> > _______________________________________________
>>> >
>>> > Seqfan Mailing list - http://list.seqfan.eu/
>>> >
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>
>


From njasloane at gmail.com  Wed Feb 11 23:55:25 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 17:55:25 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <1423692357.25896.YahooMailNeo@web185002.mail.gq1.yahoo.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
 <1423692357.25896.YahooMailNeo@web185002.mail.gq1.yahoo.com>
Message-ID: <CAAOnSgSSGykvFU3HHuuSDG0Ph6Scr6EA1nu_E54-THuT6QUEbQ@mail.gmail.com>

Good point, about discouraging human readers.

How about something like this? The machine-generated
cross-references could say:

Cf. (generated automatically): A234111, A234112, ...

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 5:05 PM, Ron Hardin <rhhardin at att.net> wrote:

> It's easy to add the %Y lines (done!) to the generating programs but it
> changes how you look at the line if it's an index of mentions above rather
> than something you might want to look at as decided by a human.  Either way
> is okay.  It just changes the use.
>
> The count-against is that you lose the human editor, and so may skip them
> all because so many are useless.
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
> >________________________________
> > From: Neil Sloane <njasloane at gmail.com>
> >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >Sent: Wednesday, February 11, 2015 3:35 PM
> >Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> Hardin
> >
> >
> >I cannot understand why there is ever an objection to
> >cross-references.
> >
> >If you are using the OEIS for
> >what it chiefly intended for, its main purpose, which is to help
> >you (very often, me) understand a sequence that has come
> >up in your work, then any hint at all is potentially valuable.
> >
> >A cross-reference is like someone whispering to you, "I don't know if it
> >will help, but did you look at A...... ? "
> >
> >And they should all be listed in the cross-reference section,
> >so it is easy to find them.
> >
> >
> >
> >Best regards
> >Neil
> >
> >Neil J. A. Sloane, President, OEIS Foundation.
> >11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> >Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> >Phone: 732 828 6098; home page: http://NeilSloane.com
> >Email: njasloane at gmail.com
> >
> >
> >On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters <
> franktaw at netscape.net>
> >wrote:
> >
> >> Just as a point of reference, a search for "A000217 -xref:A000217" gives
> >> 933 matches, out of 2699 that match "A000217".
> >>
> >> Franklin T. Adams-Watters
> >>
> >> -----Original Message-----
> >> From: Neil Sloane <njasloane at gmail.com>
> >> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >> Sent: Wed, Feb 11, 2015 1:41 pm
> >> Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> Hardin
> >>
> >>
> >>  I forget.  But the main reason is for humans to be able to see at a
> glance
> >> what sequences are mentioned.
> >>
> >> Best regards
> >> Neil
> >>
> >> Neil J. A. Sloane, President, OEIS Foundation.
> >> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> >> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
> NJ.
> >> Phone: 732 828 6098; home page: http://NeilSloane.com
> >> Email: njasloane at gmail.com
> >>
> >>
> >> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
> >> charles.greathouse at case.edu> wrote:
> >>
> >>  What part of Russ' code work improperly when a sequence is in an
> >>>
> >> entry but
> >>
> >>> not the xref field?
> >>>
> >>> Charles Greathouse
> >>> Analyst/Programmer
> >>> Case Western Reserve University
> >>>
> >>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
> >>>
> >> wrote:
> >>
> >>>
> >>> > Just to clarify one point:
> >>> >
> >>> > The rule is that if there is a line anywhere in the entry that
> >>> > mentions A123456, then Cf. A123456 should also appear in the
> >>> > cross-references section.
> >>> >
> >>> > (there are two good reasons: so Russ's code works
> >>> > properly, and so the user can easily see if A123456 is
> >>> > referred to anywhere in the entry without having to search through
> >>>
> >> every
> >>
> >>> > line)
> >>> >
> >>> > Best regards
> >>> > Neil
> >>> >
> >>> > Neil J. A. Sloane, President, OEIS Foundation.
> >>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> >>> > Also Visiting Scientist, Math. Dept., Rutgers University,
> >>>
> >> Piscataway, NJ.
> >>
> >>> > Phone: 732 828 6098; home page: http://NeilSloane.com
> >>> > Email: njasloane at gmail.com
> >>> >
> >>> >
> >>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
> >>>
> >> wrote:
> >>
> >>> >
> >>> > > I agree than any specific case can benefit from two-way links,
> >>>
> >> but not
> >>
> >>> in
> >>> > > general.  At least it seems that way to me.
> >>> > >
> >>> > >
> >>> > > I don't understand the first paragraph problem you describe below.
> >>> > > Clicking "refs" in the header of the table gives you a nice page
> >>>
> >> with
> >>
> >>> all
> >>> > > the rows and columns and diagonals expanded for you, as well as
> >>>
> >> any
> >>
> >>> > foreign
> >>> > > sequence that happens to reference inwards.
> >>> > >
> >>> > >
> >>> > > rhhardin at mindspring.com
> >>> > > rhhardin at att.net (either)
> >>> > >
> >>> > >
> >>> > > >________________________________
> >>> > > > From: M. F. Hasler <seqfan at hasler.fr>
> >>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
> >>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
> >>>
> >> R. H.
> >>
> >>> > > Hardin
> >>> > > >
> >>> > > >
> >>> > > >Ron,
> >>> > > >
> >>> > > >I am also personally against duplicating links (really never
> >>> > > >understood why an A-number put somewhere in comment or formula
> >>>
> >> should
> >>
> >>> > > >be repeated in Xrefs), but it is nonetheless handy to have the
> >>>
> >> links
> >>
> >>> > > >to the column sequences because else you have to do a search
> >>>
> >> with only
> >>
> >>> > > >the sequence number in order to find them via the backlink, but
> >>>
> >> often
> >>
> >>> > > >you come there following a link and not doing a search (and it is
> >>> > > >somehow counter-intuitive to copy-paste the number of the
> >>>
> >> sequence
> >>
> >>> > > >already displayed on the screen again into the search box...).
> >>> > > >
> >>> > > >Also, in the present case there was no link to the tables
> >>>
> >> A250676 and
> >>
> >>> > > >A250691 with almost identical definition, and they would not pop
> >>>
> >> up
> >>
> >>> > > >doing a search for the other sequence numbers.
> >>> > > >
> >>> > > >I also agree on the "significance" issue, and it is painfully to
> >>>
> >> have
> >>
> >>> > > >a bunch of sequence numbers in the Xrefs without knowing why
> >>>
> >> they are
> >>
> >>> > > >there. But with 2-3 words of explanation or just hints, this is
> >>>
> >> a true
> >>
> >>> > > >added value, I think.
> >>> > > >
> >>> > > >Maximilian
> >>> > > >
> >>> > > >
> >>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
> >>>
> >> wrote:
> >>
> >>> > > >> The row/col/diag series always link to the table, so the refs
> >>>
> >> link
> >>
> >>> in
> >>> > > the table will find them.
> >>> > > >>
> >>> > > >> It always seemed like needless clutter to link the other way
> >>> without a
> >>> > > reason beyond existence.  It seems to claim significance beyond
> >>>
> >> that.
> >>
> >>> > > >>
> >>> > > >> The inbound links by contrast say that there are more like
> >>>
> >> this, in
> >>
> >>> > > this family.
> >>> > > >>
> >>> > > >>
> >>> > > >> rhhardin at mindspring.com
> >>> > > >> rhhardin at att.net (either)
> >>> > > >>
> >>> > > >>
> >>> > > >>>________________________________
> >>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
> >>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
> >>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
> >>>
> >> R. H.
> >>
> >>> > > Hardin
> >>> > > >>>
> >>> > > >>>
> >>> > > >>>I added your comment in A250544, and also several missing
> >>> > > >>>cross-references to sequences which list the rows/cols.
> >>> > > >>>It would be nice if others could edit related sequences in a
> >>>
> >> similar
> >>
> >>> > > manner.
> >>> > > >>>
> >>> > > >>>Maximilian
> >>> > > >>>
> >>> > > >>>
> >>> > > >>
> >>> > > >> _______________________________________________
> >>> > > >>
> >>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> >
> >>> > > >
> >>> > > >
> >>> > > >
> >>> > > >
> >>> > > >
> >>> > > >_______________________________________________
> >>> > > >
> >>> > > >Seqfan Mailing list - http://list.seqfan.eu/
> >>> > > >
> >>> > > >
> >>> > > >
> >>> > >
> >>> > > _______________________________________________
> >>> > >
> >>> > > Seqfan Mailing list - http://list.seqfan.eu/
> >>> > >
> >>> >
> >>> > _______________________________________________
> >>> >
> >>> > Seqfan Mailing list - http://list.seqfan.eu/
> >>> >
> >>>
> >>> _______________________________________________
> >>>
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
> >>>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >_______________________________________________
> >
> >Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From michel.marcus at free.fr  Wed Feb 11 21:15:17 2015
From: michel.marcus at free.fr (michel.marcus at free.fr)
Date: Wed, 11 Feb 2015 21:15:17 +0100 (CET)
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <1588911053.534795074.1423685610707.JavaMail.root@spooler7-g27.priv.proxad.net>
Message-ID: <115735703.534802904.1423685717411.JavaMail.root@spooler7-g27.priv.proxad.net>

I guess that's why the "refs" link in A000217 is: A000217 -id:A000217 . 


Michel Marcus 


From zbi74583.boat at orange.zero.jp  Mon Feb  9 07:43:48 2015
From: zbi74583.boat at orange.zero.jp (zbi74583.boat at orange.zero.jp)
Date: Mon, 9 Feb 2015 15:43:48 +0900 (JST)
Subject: [seqfan] Generalized Amicable Number
Message-ID: <65391.114.49.34.179.1423464228.squirrel@webmail.zero.jp>

    Hi,Seqfans
    I genaralized Amicable Number as follows

    (-1)Sigma(x)=(-1)Sigma(y)=8/5*(x*y)^(1/2)

    The definition of (-1)Sigma(x) is here A049060

    I computed it by hand

    x = 5^2*11*29*2^2*3^2
    y = 5^2*11*29*7^2

    x = y
      = 2^2*3^3*5^2*7*19*29

    x = 3^3*7*19*29*2^4
    y = 3^3*7*19*29*5^2

    Could anyon confirm them and compute
    more term?



    Yasutoshi




From jfb at brennen.net  Thu Feb 12 18:05:53 2015
From: jfb at brennen.net (Jack Brennen)
Date: Thu, 12 Feb 2015 09:05:53 -0800
Subject: [seqfan] Re: Generalized Amicable Number
In-Reply-To: <65391.114.49.34.179.1423464228.squirrel@webmail.zero.jp>
References: <65391.114.49.34.179.1423464228.squirrel@webmail.zero.jp>
Message-ID: <54DCDD71.6050003@brennen.net>

For your first pair, it seems that they satisfy the equation:

    (-1)Sigma(x)=(-1)Sigma(y)=4/3*(x*y)^(1/2)

I can confirm that the other two you provided are correct.

Is it possible that the ratio of 8/5 doesn't need to be
fixed, but instead of the form 2-2/p ?  Given the significance
of the "-2" in the computation of (-1)Sigma(x), I could imagine
how that might make sense.

Pairs that I found that satisfy the equation at the given 8/5
ratio include:

x = y = 2^3*3^3*5*13*19

x = 3^3*7*19*29*2^4
y = 3^3*7*19*29*5^2           {Your 3rd pair}

x = y = 2^4*3^3*5*7*19*29
x = y = 2^2*3^3*5^2*7*19*29   {Your 2nd pair}
x = y = 2^2*3^3*5^3*7*11*19
x = y = 2^6*3*5^5*61
x = y = 2^3*3^2*5^2*7*11*13*29


On 2/8/2015 10:43 PM, zbi74583.boat at orange.zero.jp wrote:
>      Hi,Seqfans
>      I genaralized Amicable Number as follows
>
>      (-1)Sigma(x)=(-1)Sigma(y)=8/5*(x*y)^(1/2)
>
>      The definition of (-1)Sigma(x) is here A049060
>
>      I computed it by hand
>
>      x = 5^2*11*29*2^2*3^2
>      y = 5^2*11*29*7^2
>
>      x = y
>        = 2^2*3^3*5^2*7*19*29
>
>      x = 3^3*7*19*29*2^4
>      y = 3^3*7*19*29*5^2
>
>      Could anyon confirm them and compute
>      more term?
>
>
>
>      Yasutoshi
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>



From hpd at hpdale.org  Sat Feb 14 01:59:34 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 14 Feb 2015 00:59:34 +0000
Subject: [seqfan] A133579
Message-ID: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>

	I cannot figure out how to generate the terms of the above sequence from its definition.
	Best,
	Harvey


From franktaw at netscape.net  Sat Feb 14 02:33:18 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Fri, 13 Feb 2015 20:33:18 -0500
Subject: [seqfan] Re: A133579
In-Reply-To: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
Message-ID: <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>

The definition is clearly wrong, since gcd(n,a(n-1)) always divides 
a(n-1).

A133580 seems to be related, and may provide a clue. (BTW, the offset 
for A133580 is wrong; from the definition it should be 0.)

Franklin T. Adams-Watters

-----Original Message-----
From: Harvey P. Dale <hpd at hpdale.org>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Feb 13, 2015 6:59 pm
Subject: [seqfan] A133579


	I cannot figure out how to generate the terms of the above sequence 
from its
definition.
	Best,
	Harvey

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From njasloane at gmail.com  Sat Feb 14 03:13:06 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Fri, 13 Feb 2015 21:13:06 -0500
Subject: [seqfan] Re: A133579
In-Reply-To: <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
Message-ID: <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>

First, about A133580: the definition was correct, and the terms were
correct, but the offset should have been 0.  I changed the offset and added
some example lines to clarify the situation.

The b-file is now wrong, unfortunately (Harvey, could you correct it?), and
probably the programs also need correcting.

Following Franklin's hint, this suggests that the correct
definition of A133579 should be:

a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime,
otherwise a(n) = a(n-1)/gcd(a(n-1),n).

This almost matches the terms, but there is a mistake at
a(6), I believe, - as Harvey noticed - so it
needs to be recomputed. (a(6) should be 1 not 9). The offset is also wrong,
it should be 0, and I will fix that.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> The definition is clearly wrong, since gcd(n,a(n-1)) always divides a(n-1).
>
> A133580 seems to be related, and may provide a clue. (BTW, the offset for
> A133580 is wrong; from the definition it should be 0.)
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Harvey P. Dale <hpd at hpdale.org>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Feb 13, 2015 6:59 pm
> Subject: [seqfan] A133579
>
>
>         I cannot figure out how to generate the terms of the above
> sequence from its
> definition.
>         Best,
>         Harvey
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Sat Feb 14 03:21:53 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Fri, 13 Feb 2015 21:21:53 -0500
Subject: [seqfan] Re: A133579
In-Reply-To: <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
 <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
Message-ID: <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>

A133058 needed  a similar correction (and lacks a b-file - Harvey?)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 13, 2015 at 9:13 PM, Neil Sloane <njasloane at gmail.com> wrote:

> First, about A133580: the definition was correct, and the terms were
> correct, but the offset should have been 0.  I changed the offset and added
> some example lines to clarify the situation.
>
> The b-file is now wrong, unfortunately (Harvey, could you correct it?),
> and probably the programs also need correcting.
>
> Following Franklin's hint, this suggests that the correct
> definition of A133579 should be:
>
> a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime,
> otherwise a(n) = a(n-1)/gcd(a(n-1),n).
>
> This almost matches the terms, but there is a mistake at
> a(6), I believe, - as Harvey noticed - so it
> needs to be recomputed. (a(6) should be 1 not 9). The offset is also wrong,
> it should be 0, and I will fix that.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters <
> franktaw at netscape.net> wrote:
>
>> The definition is clearly wrong, since gcd(n,a(n-1)) always divides
>> a(n-1).
>>
>> A133580 seems to be related, and may provide a clue. (BTW, the offset for
>> A133580 is wrong; from the definition it should be 0.)
>>
>> Franklin T. Adams-Watters
>>
>>
>> -----Original Message-----
>> From: Harvey P. Dale <hpd at hpdale.org>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Fri, Feb 13, 2015 6:59 pm
>> Subject: [seqfan] A133579
>>
>>
>>         I cannot figure out how to generate the terms of the above
>> sequence from its
>> definition.
>>         Best,
>>         Harvey
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>


From hpd at hpdale.org  Sat Feb 14 17:33:23 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 14 Feb 2015 16:33:23 +0000
Subject: [seqfan] Re: A133579
In-Reply-To: <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
 <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
 <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>
Message-ID: <CY1PR0401MB106882AC1B98B9DFA0598C2FC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>

	I checked the Mma programs for A133580 and they are still okay even after the offset was changed.  I recomputed the b-file to reflect the changed offset and the new b-file has now been uploaded.
	I cannot generate the terms of A133579 even using Neil's revised definition so I suspect the revised definition is still not correct.
	Best,
	Harvey

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil Sloane
Sent: Friday, February 13, 2015 9:22 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: A133579

A133058 needed  a similar correction (and lacks a b-file - Harvey?)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 13, 2015 at 9:13 PM, Neil Sloane <njasloane at gmail.com> wrote:

> First, about A133580: the definition was correct, and the terms were 
> correct, but the offset should have been 0.  I changed the offset and 
> added some example lines to clarify the situation.
>
> The b-file is now wrong, unfortunately (Harvey, could you correct 
> it?), and probably the programs also need correcting.
>
> Following Franklin's hint, this suggests that the correct definition 
> of A133579 should be:
>
> a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime, 
> otherwise a(n) = a(n-1)/gcd(a(n-1),n).
>
> This almost matches the terms, but there is a mistake at a(6), I 
> believe, - as Harvey noticed - so it needs to be recomputed. (a(6) 
> should be 1 not 9). The offset is also wrong, it should be 0, and I 
> will fix that.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters < 
> franktaw at netscape.net> wrote:
>
>> The definition is clearly wrong, since gcd(n,a(n-1)) always divides 
>> a(n-1).
>>
>> A133580 seems to be related, and may provide a clue. (BTW, the offset 
>> for
>> A133580 is wrong; from the definition it should be 0.)
>>
>> Franklin T. Adams-Watters
>>
>>
>> -----Original Message-----
>> From: Harvey P. Dale <hpd at hpdale.org>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Fri, Feb 13, 2015 6:59 pm
>> Subject: [seqfan] A133579
>>
>>
>>         I cannot figure out how to generate the terms of the above 
>> sequence from its definition.
>>         Best,
>>         Harvey
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/

From hpd at hpdale.org  Sat Feb 14 17:40:31 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 14 Feb 2015 16:40:31 +0000
Subject: [seqfan] A133058
Message-ID: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>

	I provided a Mma program and a b-file for the above sequence.
	Best,
	Harvey


From njasloane at gmail.com  Sat Feb 14 18:33:11 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Sat, 14 Feb 2015 12:33:11 -0500
Subject: [seqfan] Re: A133579
In-Reply-To: <CY1PR0401MB106882AC1B98B9DFA0598C2FC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
 <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
 <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>
 <CY1PR0401MB106882AC1B98B9DFA0598C2FC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
Message-ID: <CAAOnSgTWGu-YzW2uEPx-OGpN9eGYvh70sp+uirLexCwUUs3f5A@mail.gmail.com>

Harvey, Thanks for your work on A133580 and A133058.  As for A133579, I
corrected the terms and added a companion sequence A253092.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Feb 14, 2015 at 11:33 AM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         I checked the Mma programs for A133580 and they are still okay
> even after the offset was changed.  I recomputed the b-file to reflect the
> changed offset and the new b-file has now been uploaded.
>         I cannot generate the terms of A133579 even using Neil's revised
> definition so I suspect the revised definition is still not correct.
>         Best,
>         Harvey
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil
> Sloane
> Sent: Friday, February 13, 2015 9:22 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: A133579
>
> A133058 needed  a similar correction (and lacks a b-file - Harvey?)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 13, 2015 at 9:13 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > First, about A133580: the definition was correct, and the terms were
> > correct, but the offset should have been 0.  I changed the offset and
> > added some example lines to clarify the situation.
> >
> > The b-file is now wrong, unfortunately (Harvey, could you correct
> > it?), and probably the programs also need correcting.
> >
> > Following Franklin's hint, this suggests that the correct definition
> > of A133579 should be:
> >
> > a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime,
> > otherwise a(n) = a(n-1)/gcd(a(n-1),n).
> >
> > This almost matches the terms, but there is a mistake at a(6), I
> > believe, - as Harvey noticed - so it needs to be recomputed. (a(6)
> > should be 1 not 9). The offset is also wrong, it should be 0, and I
> > will fix that.
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters <
> > franktaw at netscape.net> wrote:
> >
> >> The definition is clearly wrong, since gcd(n,a(n-1)) always divides
> >> a(n-1).
> >>
> >> A133580 seems to be related, and may provide a clue. (BTW, the offset
> >> for
> >> A133580 is wrong; from the definition it should be 0.)
> >>
> >> Franklin T. Adams-Watters
> >>
> >>
> >> -----Original Message-----
> >> From: Harvey P. Dale <hpd at hpdale.org>
> >> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >> Sent: Fri, Feb 13, 2015 6:59 pm
> >> Subject: [seqfan] A133579
> >>
> >>
> >>         I cannot figure out how to generate the terms of the above
> >> sequence from its definition.
> >>         Best,
> >>         Harvey
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From hpd at hpdale.org  Sat Feb 14 19:26:30 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 14 Feb 2015 18:26:30 +0000
Subject: [seqfan] Re: A133579
In-Reply-To: <CAAOnSgTWGu-YzW2uEPx-OGpN9eGYvh70sp+uirLexCwUUs3f5A@mail.gmail.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
 <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
 <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>
 <CY1PR0401MB106882AC1B98B9DFA0598C2FC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CAAOnSgTWGu-YzW2uEPx-OGpN9eGYvh70sp+uirLexCwUUs3f5A@mail.gmail.com>
Message-ID: <CY1PR0401MB1068D5C8635258D0EE276354C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>

Neil:
	I added a Mma program for each of A133579 and A253092 and a b-file for the former.
	Best,
	Harvey

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil Sloane
Sent: Saturday, February 14, 2015 12:33 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: A133579

Harvey, Thanks for your work on A133580 and A133058.  As for A133579, I corrected the terms and added a companion sequence A253092.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Feb 14, 2015 at 11:33 AM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         I checked the Mma programs for A133580 and they are still okay 
> even after the offset was changed.  I recomputed the b-file to reflect 
> the changed offset and the new b-file has now been uploaded.
>         I cannot generate the terms of A133579 even using Neil's 
> revised definition so I suspect the revised definition is still not correct.
>         Best,
>         Harvey
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil 
> Sloane
> Sent: Friday, February 13, 2015 9:22 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: A133579
>
> A133058 needed  a similar correction (and lacks a b-file - Harvey?)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 13, 2015 at 9:13 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > First, about A133580: the definition was correct, and the terms were 
> > correct, but the offset should have been 0.  I changed the offset 
> > and added some example lines to clarify the situation.
> >
> > The b-file is now wrong, unfortunately (Harvey, could you correct 
> > it?), and probably the programs also need correcting.
> >
> > Following Franklin's hint, this suggests that the correct definition 
> > of A133579 should be:
> >
> > a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime, 
> > otherwise a(n) = a(n-1)/gcd(a(n-1),n).
> >
> > This almost matches the terms, but there is a mistake at a(6), I 
> > believe, - as Harvey noticed - so it needs to be recomputed. (a(6) 
> > should be 1 not 9). The offset is also wrong, it should be 0, and I 
> > will fix that.
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters < 
> > franktaw at netscape.net> wrote:
> >
> >> The definition is clearly wrong, since gcd(n,a(n-1)) always divides 
> >> a(n-1).
> >>
> >> A133580 seems to be related, and may provide a clue. (BTW, the 
> >> offset for
> >> A133580 is wrong; from the definition it should be 0.)
> >>
> >> Franklin T. Adams-Watters
> >>
> >>
> >> -----Original Message-----
> >> From: Harvey P. Dale <hpd at hpdale.org>
> >> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >> Sent: Fri, Feb 13, 2015 6:59 pm
> >> Subject: [seqfan] A133579
> >>
> >>
> >>         I cannot figure out how to generate the terms of the above 
> >> sequence from its definition.
> >>         Best,
> >>         Harvey
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/

From arndt at jjj.de  Sat Feb 14 20:00:11 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Sat, 14 Feb 2015 20:00:11 +0100
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAOnSgSSGykvFU3HHuuSDG0Ph6Scr6EA1nu_E54-THuT6QUEbQ@mail.gmail.com>
References: <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
 <1423692357.25896.YahooMailNeo@web185002.mail.gq1.yahoo.com>
 <CAAOnSgSSGykvFU3HHuuSDG0Ph6Scr6EA1nu_E54-THuT6QUEbQ@mail.gmail.com>
Message-ID: <20150214190011.GA25417@jjj.de>

[I was biting my tongue up to here]

* Neil Sloane <njasloane at gmail.com> [Feb 12. 2015 08:19]:
> Good point, about discouraging human readers.
> 
> How about something like this? The machine-generated
> cross-references could say:
> 
> Cf. (generated automatically): A234111, A234112, ...

Yes!

There will be some draw backs, e.g., when people do the
A-number dance in the formula section, e.g., writing
A000040(n) for prime(n) or (much worse) A000027(n) for n.

And pretty please un-enforce the manual adding of all crossrefs.

Best,  jj


> 
> Best regards
> Neil
> 
> [...]


From acwacw at gmail.com  Sun Feb 15 00:51:34 2015
From: acwacw at gmail.com (Allan Wechsler)
Date: Sat, 14 Feb 2015 18:51:34 -0500
Subject: [seqfan] Re: A133058
In-Reply-To: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
References: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
Message-ID: <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>

If the program and b-file are right, the sequence enters a very simple
regime at n=638.
a(638+4k) = 1, a(639+4k) = 641+4k, a(640+4k) = 1282+8k, a(641+4k) = 2, for
all k>=0.

On Sat, Feb 14, 2015 at 11:40 AM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         I provided a Mma program and a b-file for the above sequence.
>         Best,
>         Harvey
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From oeis at hasler.fr  Sun Feb 15 15:04:28 2015
From: oeis at hasler.fr (M. F. Hasler)
Date: Sun, 15 Feb 2015 10:04:28 -0400
Subject: [seqfan] Re: A133058
In-Reply-To: <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>
References: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>
Message-ID: <CABxCbJ0QmaGjLidaDxs1kJ+1vXgQThnejJYj5YHmWcKH=cQuiA@mail.gmail.com>

On Sat, Feb 14, 2015 at 7:51 PM, Allan Wechsler <acwacw at gmail.com> wrote:
> If the program and b-file are right, the sequence enters a very simple
> regime at n=638.
> a(638+4k) = 1, a(639+4k) = 641+4k, a(640+4k) = 1282+8k, a(641+4k) = 2, for
> all k>=0.

I agree with Allan's result (and added PARI code producing the same sequence).
If one defines
a(1)=1; a(n+1) = a(n) + n + 1 if a(n) and n are coprime,
otherwise a(n+1) = a(n)/gcd(a(n),n).

one gets a "trivial" sequence having this behaviour right from the start :
 1, 3, 6, 2, 1, 7, 14, 2, 1, 11, 22, 2, 1, 15, 30, 2, 1, 19,...
i.e., a(4n+1) = 1, a(4n+2) = 4n+3, a(4n+3) = 8n+6, a(4n) = 2.

which I submitted in spite of "kw: easy, dumb" as A255051 ;
Changing the +1 to +2  yields yet another (less trivial) variant,
1, 4, 2, 7, 13, 20, 10, 19, 29, 40, 4, 17, 31, 46, 23, 40, 5, ...
submitted as A255140.
-- 
Maximilian


From acwacw at gmail.com  Sun Feb 15 15:30:38 2015
From: acwacw at gmail.com (Allan Wechsler)
Date: Sun, 15 Feb 2015 09:30:38 -0500
Subject: [seqfan] Re: A133058
In-Reply-To: <CABxCbJ0QmaGjLidaDxs1kJ+1vXgQThnejJYj5YHmWcKH=cQuiA@mail.gmail.com>
References: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>
 <CABxCbJ0QmaGjLidaDxs1kJ+1vXgQThnejJYj5YHmWcKH=cQuiA@mail.gmail.com>
Message-ID: <CADy-sGFUJeFF_Mscn-QrRkeh9JgEEcVit4FJZTBC3JqDP1DC+Q@mail.gmail.com>

A comment by the author (Zizka) seems to recognize the possibility of these
period-4 regimes. This leads me to think that one might devise a
meta-sequence telling how soon the regime is entered depending on starting
values.
On Feb 15, 2015 9:05 AM, "M. F. Hasler" <oeis at hasler.fr> wrote:

> On Sat, Feb 14, 2015 at 7:51 PM, Allan Wechsler <acwacw at gmail.com> wrote:
> > If the program and b-file are right, the sequence enters a very simple
> > regime at n=638.
> > a(638+4k) = 1, a(639+4k) = 641+4k, a(640+4k) = 1282+8k, a(641+4k) = 2,
> for
> > all k>=0.
>
> I agree with Allan's result (and added PARI code producing the same
> sequence).
> If one defines
> a(1)=1; a(n+1) = a(n) + n + 1 if a(n) and n are coprime,
> otherwise a(n+1) = a(n)/gcd(a(n),n).
>
> one gets a "trivial" sequence having this behaviour right from the start :
>  1, 3, 6, 2, 1, 7, 14, 2, 1, 11, 22, 2, 1, 15, 30, 2, 1, 19,...
> i.e., a(4n+1) = 1, a(4n+2) = 4n+3, a(4n+3) = 8n+6, a(4n) = 2.
>
> which I submitted in spite of "kw: easy, dumb" as A255051 ;
> Changing the +1 to +2  yields yet another (less trivial) variant,
> 1, 4, 2, 7, 13, 20, 10, 19, 29, 40, 4, 17, 31, 46, 23, 40, 5, ...
> submitted as A255140.
> --
> Maximilian
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From oeis at hasler.fr  Sun Feb 15 16:58:43 2015
From: oeis at hasler.fr (M. F. Hasler)
Date: Sun, 15 Feb 2015 11:58:43 -0400
Subject: [seqfan] Re: A133058
In-Reply-To: <CADy-sGFUJeFF_Mscn-QrRkeh9JgEEcVit4FJZTBC3JqDP1DC+Q@mail.gmail.com>
References: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>
 <CABxCbJ0QmaGjLidaDxs1kJ+1vXgQThnejJYj5YHmWcKH=cQuiA@mail.gmail.com>
 <CADy-sGFUJeFF_Mscn-QrRkeh9JgEEcVit4FJZTBC3JqDP1DC+Q@mail.gmail.com>
Message-ID: <CABxCbJ1cOna+cxC4OFq6YcEvxiSv6Cbo_5hm6eqnX_OqG507Ow@mail.gmail.com>

On Sun, Feb 15, 2015 at 10:30 AM, Allan Wechsler <acwacw at gmail.com> wrote:
> A comment by the author (Zizka) seems to recognize the possibility of these
> period-4 regimes. This leads me to think that one might devise a
> meta-sequence telling how soon the regime is entered depending on starting
> values.

Maybe, but note that A255140 enters a different loop, of form
(1,x,2x,x) and not (1,x,2x,2).
So actually we would have (at least) these 3 variants (**)
(with ...+n  vs. +n+1 and offset/indexing a[n-1] vs a[n])
and for each of these a meta sequence, function of the respective a[1].

(**) The a(n+1) = a(n)*2+1 resp. a(n)*3 variants do not have this
looping property, but each has its own self-similarity property, which
is for the latter also explained by the simple recurrence formula I
added for A253092 = log3 A133579.
-- 
Maximilian


From rhhardin at att.net  Mon Feb 16 17:22:52 2015
From: rhhardin at att.net (Ron Hardin)
Date: Mon, 16 Feb 2015 08:22:52 -0800
Subject: [seqfan] Guess the formula T(n,k)=?
Message-ID: <1424103772.41349.YahooMailNeo@web185002.mail.gq1.yahoo.com>

This is likely to be T(n,k)=f(n)+f(k) with f() having a 2^() flavor.


Every row, column and the diagonal satisfy the same recurrence.

The solutions seem to pick every 3rd row or column for 1's and sometimes add cross rows or columns of 1's.


/tmp/eyg
T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2

Table starts
..23..22..31..43..61..88.127.184.268.391.571..835.1222.1789.2620.3838.5623.8239
..22..28..37..49..67..94.133.190.274.397.577..841.1228.1795.2626.3844.5629.8245
..31..37..46..58..76.103.142.199.283.406.586..850.1237.1804.2635.3853.5638.8254
..43..49..58..70..88.115.154.211.295.418.598..862.1249.1816.2647.3865.5650.8266
..61..67..76..88.106.133.172.229.313.436.616..880.1267.1834.2665.3883.5668.8284
..88..94.103.115.133.160.199.256.340.463.643..907.1294.1861.2692.3910.5695.8311
.127.133.142.154.172.199.238.295.379.502.682..946.1333.1900.2731.3949.5734.8350
.184.190.199.211.229.256.295.352.436.559.739.1003.1390.1957.2788.4006.5791.8407
.268.274.283.295.313.340.379.436.520.643.823.1087.1474.2041.2872.4090.5875.8491
.391.397.406.418.436.463.502.559.643.766.946.1210.1597.2164.2995.4213.5998.8614

Empirical for diagonal:
a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4) for n>5
Empirical for column k:
k=1: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4) for n>5
k=2: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=3: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=4: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=5: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=6: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=7: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)

Two solutions for n=8 k=8
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....1..1..1..1..1..1..1..1..1..1
..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....1..1..1..1..1..1..1..1..1..1
..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0


 
rhhardin at mindspring.com
rhhardin at att.net (either)


From susanne.wienand at gmail.com  Tue Feb 17 23:05:43 2015
From: susanne.wienand at gmail.com (Susanne Wienand)
Date: Tue, 17 Feb 2015 23:05:43 +0100
Subject: [seqfan] Re: Guess the formula T(n,k)=?
In-Reply-To: <1424103772.41349.YahooMailNeo@web185002.mail.gq1.yahoo.com>
References: <1424103772.41349.YahooMailNeo@web185002.mail.gq1.yahoo.com>
Message-ID: <CAH=KaNvvbFoEeH8AvtEJc9MfYLhjuipHteVR+SaHHDgF5zw2_w@mail.gmail.com>

Hello Ron,

The terms seem to be related to A000930, Narayana's cow sequence.
If decreased by 22 and then divided by 3, the terms become

.1/3....0....3....7....13....22..35..54..82..123..183..271..400..589..866..1272..1867..2739

..0.....2....5....9....15....24..37..56..84..125..185..273..402..591..868..1274..1869..2741

..3.....5....8...12....18....27..40..59..87..128..188..276..405..594..871..1277..1872..2744

..7.....9...12...16....22....31..44..63..91..132..192..280..409..598..875..1281..1876..2748

.13....15...18...22....28....37..50..69..97..138..198..286..415..604..881..1287..1882..2754

.22....24...27...31....37....46..59..78.106..147..207..295..424..613..890..1296..1891..2763

.35....37...40...44....50....59..72..91.119..160..220..308..437..626..903..1309..1904..2776

.54....56...59...63....69....78..91.110.138..179..239..327..456..645..922..1328..1923..2795

.82....84...87...91....97...106.119.138.166..207..267..355..484..673..950..1356..1951..2823

123...125..128..132...138...147.160.179.207..248..308..396..525..714..991..1397..1992..2864

Most differences (except upper left corner) along the columns and the rows
seem to match with A000930:
*2*, *3*, *4*, *6*, *9*, *13*, *19*, *28*, 41, 60, 88, 129, 189, 277, 406,
595, 872, 1278

T(2,2) - T(2,1) = 2 - 0 = 2
T(2,3) - T(2,2) = 5 - 2 = 3
T(2,4) - T(2,3) = 9 - 5 = 4
...

I hope this can help to find the formula.

Regards
Susanne

2015-02-16 17:22 GMT+01:00 Ron Hardin <rhhardin at att.net>:

> This is likely to be T(n,k)=f(n)+f(k) with f() having a 2^() flavor.
>
>
> Every row, column and the diagonal satisfy the same recurrence.
>
> The solutions seem to pick every 3rd row or column for 1's and sometimes
> add cross rows or columns of 1's.
>
>
> /tmp/eyg
> T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum
> 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2
>
> Table starts
>
> ..23..22..31..43..61..88.127.184.268.391.571..835.1222.1789.2620.3838.5623.8239
>
> ..22..28..37..49..67..94.133.190.274.397.577..841.1228.1795.2626.3844.5629.8245
>
> ..31..37..46..58..76.103.142.199.283.406.586..850.1237.1804.2635.3853.5638.8254
>
> ..43..49..58..70..88.115.154.211.295.418.598..862.1249.1816.2647.3865.5650.8266
>
> ..61..67..76..88.106.133.172.229.313.436.616..880.1267.1834.2665.3883.5668.8284
>
> ..88..94.103.115.133.160.199.256.340.463.643..907.1294.1861.2692.3910.5695.8311
>
> .127.133.142.154.172.199.238.295.379.502.682..946.1333.1900.2731.3949.5734.8350
>
> .184.190.199.211.229.256.295.352.436.559.739.1003.1390.1957.2788.4006.5791.8407
>
> .268.274.283.295.313.340.379.436.520.643.823.1087.1474.2041.2872.4090.5875.8491
>
> .391.397.406.418.436.463.502.559.643.766.946.1210.1597.2164.2995.4213.5998.8614
>
> Empirical for diagonal:
> a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4) for n>5
> Empirical for column k:
> k=1: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4) for n>5
> k=2: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=3: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=4: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=5: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=6: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=7: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
>
> Two solutions for n=8 k=8
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
> ..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....1..1..1..1..1..1..1..1..1..1
> ..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....1..1..1..1..1..1..1..1..1..1
> ..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
>
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From 2stepan at rambler.ru  Thu Feb 19 15:55:11 2015
From: 2stepan at rambler.ru (=?koi8-r?B?wNLJyiDHxdLB08nNz9c=?=)
Date: Thu, 19 Feb 2015 17:55:11 +0300
Subject: [seqfan] 4xy + 6x - 1
In-Reply-To: <1424357709.807527.19545.27241@mail.rambler.ru>
References: <1424357709.807527.19545.27241@mail.rambler.ru>
Message-ID: <1424357710.983999.15355.48162@mail.rambler.ru>


Dear SeqFans, 

Primes not of the form 4xy + 6x - 1: 2, 3, 7, 31, ...

What in the next one?

Thanks. JSG

From olivier.gerard at gmail.com  Thu Feb 19 16:56:24 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Thu, 19 Feb 2015 16:56:24 +0100
Subject: [seqfan] Re: 4xy + 6x - 1
In-Reply-To: <1424357710.983999.15355.48162@mail.rambler.ru>
References: <1424357709.807527.19545.27241@mail.rambler.ru>
 <1424357710.983999.15355.48162@mail.rambler.ru>
Message-ID: <CAAcpPSbcSpMF2jvhbMuMLJ7YdLeifK7RJWcmK4XQK67CSmGU0g@mail.gmail.com>

Youri,

If you restrict to x, y, 0 or positive integers,
your list is certainly 2 plus Mersenne primes,
anyway the next one should be 127.

If you allow x, y any integer, you will probably find
that only 2 cannot be represented this way.

Olivier


On Thu, Feb 19, 2015 at 3:55 PM, ???? ????????? <2stepan at rambler.ru> wrote:

>
> Dear SeqFans,
> Primes not of the form 4xy + 6x - 1: 2, 3, 7, 31, ...
>
> What in the next one?
>
> Thanks. JSG
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From rselcoe at entouchonline.net  Thu Feb 19 17:04:45 2015
From: rselcoe at entouchonline.net (Bob Selcoe)
Date: Thu, 19 Feb 2015 10:04:45 -0600
Subject: [seqfan] Re: 4xy + 6x - 1
In-Reply-To: <1424357710.983999.15355.48162@mail.rambler.ru>
References: <1424357709.807527.19545.27241@mail.rambler.ru>
 <1424357710.983999.15355.48162@mail.rambler.ru>
Message-ID: <37A5F4897FEB4645829AF7CB37B94C93@OwnerPC>

Hello,

127.  The sequence will be 2 and the Mersenne primes.  The equation is 
2x(2y+3)-1, which is all the even numbers times all the odd numbers minus 1. 
These are all the odd numbers except 2^n-1 which, when prime, are the 
Mersennes.

Best,
Bob Selcoe

--------------------------------------------------
From: "???? ?????????" <2stepan at rambler.ru>
Sent: Thursday, February 19, 2015 8:55 AM
To: <seqfan at list.seqfan.eu>
Subject: [seqfan] 4xy + 6x - 1

>
> Dear SeqFans,
> Primes not of the form 4xy + 6x - 1: 2, 3, 7, 31, ...
>
> What in the next one?
>
> Thanks. JSG
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
> 


From reddwarf2956 at yahoo.com  Fri Feb 20 10:53:42 2015
From: reddwarf2956 at yahoo.com (John W. Nicholson)
Date: Fri, 20 Feb 2015 09:53:42 +0000 (UTC)
Subject: [seqfan] Is there any problems with this proof?
Message-ID: <241484269.320541.1424426022835.JavaMail.yahoo@mail.yahoo.com>

Below is a proof based on A005250(n ) of the OEIS.? Can someone look at it and tell me if it true?
http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
If it is true, an edit of A005250 comments is needed.? 

Related:
https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1


?John W. Nicholson


From felix.froe at googlemail.com  Fri Feb 20 11:10:10 2015
From: felix.froe at googlemail.com (=?UTF-8?Q?Felix_Fr=C3=B6hlich?=)
Date: Fri, 20 Feb 2015 11:10:10 +0100
Subject: [seqfan] Additional keywords for OEIS
Message-ID: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>

Dear SeqFans,

as some of you might know, there has been some discussion about the
addition of additional keywords to the OEIS. Most of what I found regarding
that discussion has taken place in the userspace of Charles Greathouse in
the OEIS Wiki. See
https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and the
corresponding talk pages.

Personally I think the possibility to refine OEIS searches via specific
keywords is very useful and I often make use of that feature. The addition
of new keywords would allow one to get even more relevant results. For
example, Alex Ratushnyak in 2013 suggested the addition of a keyword 'prim'
that would allow one to find all sequences where all terms are prime. Two
obvious candidates for this keyword would be sequences like A000040
or A000043.

As I am not familiar with the technical aspects behind the OEIS database, I
would like to know how much work it would be to add new keywords to the
OEIS or whether it is technically possible at all (maybe it's just like
running an SQL query to update some database table, or maybe it requires
some complete rewrite of some part of the software underlying the OEIS, I
do not know). If it is technically feasible to do this and if those who
maintain the technical integrity of the OEIS think such a step would be
desirable, then as a next step we could collect suggestions regarding which
keywords would be useful.

What do others think?

Best regards

Felix Fr?hlich


From maximilian.hasler at gmail.com  Fri Feb 20 12:19:51 2015
From: maximilian.hasler at gmail.com (Maximilian F. Hasler)
Date: Fri, 20 Feb 2015 07:19:51 -0400
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
Message-ID: <CAOPi3QLUZDHy2CAgQ4j1UV1zCCbooqBJa=pOQbExrBE0KraOHw@mail.gmail.com>

I'm quite in favor of this, and more.
I developed some thoughts on
https://oeis.org/wiki/User:M._F._Hasler/Work_in_progress/Improvements_of_OEIS
I think switching to freely definable categories could be an interesting
alternative/complement to (or way of maintaining) the currently existing
index.

Maximilian
Le 20 f?vr. 2015 06:11, "Felix Fr?hlich" <felix.froe at googlemail.com> a
?crit :

> Dear SeqFans,
>
> as some of you might know, there has been some discussion about the
> addition of additional keywords to the OEIS. Most of what I found regarding
> that discussion has taken place in the userspace of Charles Greathouse in
> the OEIS Wiki. See
> https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and the
> corresponding talk pages.
>
> Personally I think the possibility to refine OEIS searches via specific
> keywords is very useful and I often make use of that feature. The addition
> of new keywords would allow one to get even more relevant results. For
> example, Alex Ratushnyak in 2013 suggested the addition of a keyword 'prim'
> that would allow one to find all sequences where all terms are prime. Two
> obvious candidates for this keyword would be sequences like A000040
> or A000043.
>
> As I am not familiar with the technical aspects behind the OEIS database, I
> would like to know how much work it would be to add new keywords to the
> OEIS or whether it is technically possible at all (maybe it's just like
> running an SQL query to update some database table, or maybe it requires
> some complete rewrite of some part of the software underlying the OEIS, I
> do not know). If it is technically feasible to do this and if those who
> maintain the technical integrity of the OEIS think such a step would be
> desirable, then as a next step we could collect suggestions regarding which
> keywords would be useful.
>
> What do others think?
>
> Best regards
>
> Felix Fr?hlich
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From franktaw at netscape.net  Fri Feb 20 19:18:04 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Fri, 20 Feb 2015 13:18:04 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
Message-ID: <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>

While I'm not familiar with the code being used, making new keywords 
available can't be very difficult.

Getting the keyword assigned to all and only those sequences where it 
belongs is another matter, ranging from a bit trickier than you might 
think to requiring many man-hours. For the example below, the process 
could be automated with 99%+ accuracy. I don't know of any off hand, 
but there are probably sequences in the database whose first non-prime 
member comes quite late. The process also has to be able to deal with 
sequences having very large terms. One keyword I have considered, 
"fact", for those sequences which depend on factorization, in the same 
way that "base" sequences depend on representation as numerals, would 
be very difficult to get anywhere close to being right.

Franklin T. Adams-Watters

-----Original Message-----
From: Felix Fr?hlich <felix.froe at googlemail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Feb 20, 2015 5:10 am
Subject: [seqfan] Additional keywords for OEIS


Dear SeqFans,

as some of you might know, there has been some discussion about the
addition of additional keywords to the OEIS. Most of what I found 
regarding
that discussion has taken place in the userspace of Charles Greathouse 
in
the OEIS Wiki. See
https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and 
the
corresponding talk pages.

Personally I think the possibility to refine OEIS searches via specific
keywords is very useful and I often make use of that feature. The 
addition
of new keywords would allow one to get even more relevant results. For
example, Alex Ratushnyak in 2013 suggested the addition of a keyword 
'prim'
that would allow one to find all sequences where all terms are prime. 
Two
obvious candidates for this keyword would be sequences like A000040
or A000043.

As I am not familiar with the technical aspects behind the OEIS 
database, I
would like to know how much work it would be to add new keywords to the
OEIS or whether it is technically possible at all (maybe it's just like
running an SQL query to update some database table, or maybe it requires
some complete rewrite of some part of the software underlying the OEIS, 
I
do not know). If it is technically feasible to do this and if those who
maintain the technical integrity of the OEIS think such a step would be
desirable, then as a next step we could collect suggestions regarding 
which
keywords would be useful.

What do others think?

Best regards

Felix Fr?hlich

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From njasloane at gmail.com  Fri Feb 20 18:24:10 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Fri, 20 Feb 2015 12:24:10 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
Message-ID: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>

Instead of adding more keywords, which are necessarily
rather limited, Charles and I had discussed adding
"categories".  This may be a better way to proceed.
Charles, did you think any more about how this idea might be implemented?
IIRC, you started to learn Go for that purpose?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> While I'm not familiar with the code being used, making new keywords
> available can't be very difficult.
>
> Getting the keyword assigned to all and only those sequences where it
> belongs is another matter, ranging from a bit trickier than you might think
> to requiring many man-hours. For the example below, the process could be
> automated with 99%+ accuracy. I don't know of any off hand, but there are
> probably sequences in the database whose first non-prime member comes quite
> late. The process also has to be able to deal with sequences having very
> large terms. One keyword I have considered, "fact", for those sequences
> which depend on factorization, in the same way that "base" sequences depend
> on representation as numerals, would be very difficult to get anywhere
> close to being right.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Felix Fr?hlich <felix.froe at googlemail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Feb 20, 2015 5:10 am
> Subject: [seqfan] Additional keywords for OEIS
>
>
> Dear SeqFans,
>
> as some of you might know, there has been some discussion about the
> addition of additional keywords to the OEIS. Most of what I found regarding
> that discussion has taken place in the userspace of Charles Greathouse in
> the OEIS Wiki. See
> https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and the
> corresponding talk pages.
>
> Personally I think the possibility to refine OEIS searches via specific
> keywords is very useful and I often make use of that feature. The addition
> of new keywords would allow one to get even more relevant results. For
> example, Alex Ratushnyak in 2013 suggested the addition of a keyword 'prim'
> that would allow one to find all sequences where all terms are prime. Two
> obvious candidates for this keyword would be sequences like A000040
> or A000043.
>
> As I am not familiar with the technical aspects behind the OEIS database, I
> would like to know how much work it would be to add new keywords to the
> OEIS or whether it is technically possible at all (maybe it's just like
> running an SQL query to update some database table, or maybe it requires
> some complete rewrite of some part of the software underlying the OEIS, I
> do not know). If it is technically feasible to do this and if those who
> maintain the technical integrity of the OEIS think such a step would be
> desirable, then as a next step we could collect suggestions regarding which
> keywords would be useful.
>
> What do others think?
>
> Best regards
>
> Felix Fr?hlich
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From franktaw at netscape.net  Fri Feb 20 19:36:26 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Fri, 20 Feb 2015 13:36:26 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
Message-ID: <8D21B4AE31E7FE1-23D4-8FBC5@webmail-vm077.sysops.aol.com>

I suggested some time ago linking keywords and the index. One would 
enter a "keyword" for the sequence, and this would automatically create 
an index entry for it. The keywords on search screens could then be 
live links to the index entries. (One would have to manually create the 
index entry itself and define its associated keyword.)

Franklin T. Adams-Watters

-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Feb 20, 2015 12:25 pm
Subject: [seqfan] Re: Additional keywords for OEIS


Instead of adding more keywords, which are necessarily
rather limited, Charles and I had discussed adding
"categories".  This may be a better way to proceed.
Charles, did you think any more about how this idea might be 
implemented?
IIRC, you started to learn Go for that purpose?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters 
<franktaw at netscape.net>
wrote:

> While I'm not familiar with the code being used, making new keywords
> available can't be very difficult.
>
> Getting the keyword assigned to all and only those sequences where it
> belongs is another matter, ranging from a bit trickier than you might 
think
> to requiring many man-hours. For the example below, the process could 
be
> automated with 99%+ accuracy. I don't know of any off hand, but there 
are
> probably sequences in the database whose first non-prime member comes 
quite
> late. The process also has to be able to deal with sequences having 
very
> large terms. One keyword I have considered, "fact", for those 
sequences
> which depend on factorization, in the same way that "base" sequences 
depend
> on representation as numerals, would be very difficult to get anywhere
> close to being right.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Felix Fr?hlich <felix.froe at googlemail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Feb 20, 2015 5:10 am
> Subject: [seqfan] Additional keywords for OEIS
>
>
> Dear SeqFans,
>
> as some of you might know, there has been some discussion about the
> addition of additional keywords to the OEIS. Most of what I found 
regarding
> that discussion has taken place in the userspace of Charles 
Greathouse in
> the OEIS Wiki. See
> https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and 
the
> corresponding talk pages.
>
> Personally I think the possibility to refine OEIS searches via 
specific
> keywords is very useful and I often make use of that feature. The 
addition
> of new keywords would allow one to get even more relevant results. For
> example, Alex Ratushnyak in 2013 suggested the addition of a keyword 
'prim'
> that would allow one to find all sequences where all terms are prime. 
Two
> obvious candidates for this keyword would be sequences like A000040
> or A000043.
>
> As I am not familiar with the technical aspects behind the OEIS 
database, I
> would like to know how much work it would be to add new keywords to 
the
> OEIS or whether it is technically possible at all (maybe it's just 
like
> running an SQL query to update some database table, or maybe it 
requires
> some complete rewrite of some part of the software underlying the 
OEIS, I
> do not know). If it is technically feasible to do this and if those 
who
> maintain the technical integrity of the OEIS think such a step would 
be
> desirable, then as a next step we could collect suggestions regarding 
which
> keywords would be useful.
>
> What do others think?
>
> Best regards
>
> Felix Fr?hlich
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From r.rosenthal at web.de  Fri Feb 20 20:30:19 2015
From: r.rosenthal at web.de (Rainer Rosenthal)
Date: Fri, 20 Feb 2015 20:30:19 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
Message-ID: <54E78B4B.8050303@web.de>

Am 20.02.2015 um 18:24 schrieb Neil Sloane:
> ... Charles and I had discussed adding "categories". 
> Charles, did you think any more about how this idea might be implemented?
> IIRC, you started to learn Go for that purpose?

What has the game of Go to do with this?
I love Go, so I am very interested.

Cheers,
Rainer




From jean-paul.allouche at imj-prg.fr  Fri Feb 20 20:37:12 2015
From: jean-paul.allouche at imj-prg.fr (jean-paul allouche)
Date: Fri, 20 Feb 2015 20:37:12 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <54E78B4B.8050303@web.de>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <54E78B4B.8050303@web.de>
Message-ID: <54E78CE8.2080909@imj-prg.fr>

Hi

Go is a programming language, see, e.g., https://golang.org
best
jean-paul


Le 20/02/15 20:30, Rainer Rosenthal a ?crit :
> Am 20.02.2015 um 18:24 schrieb Neil Sloane:
>> ... Charles and I had discussed adding "categories".
>> Charles, did you think any more about how this idea might be implemented?
>> IIRC, you started to learn Go for that purpose?
> What has the game of Go to do with this?
> I love Go, so I am very interested.
>
> Cheers,
> Rainer
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



From charles.greathouse at case.edu  Fri Feb 20 20:47:49 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Fri, 20 Feb 2015 14:47:49 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
Message-ID: <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>

I like the idea of new keywords, and I like the idea of categories.
Categories seem like a great solution to many problems because they would
be (by design) extendable. Unfortunately I haven't had time to look though
this part of Russ' code, but I intend to work on this eventually.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 12:24 PM, Neil Sloane <njasloane at gmail.com> wrote:

> Instead of adding more keywords, which are necessarily
> rather limited, Charles and I had discussed adding
> "categories".  This may be a better way to proceed.
> Charles, did you think any more about how this idea might be implemented?
> IIRC, you started to learn Go for that purpose?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <
> franktaw at netscape.net>
> wrote:
>
> > While I'm not familiar with the code being used, making new keywords
> > available can't be very difficult.
> >
> > Getting the keyword assigned to all and only those sequences where it
> > belongs is another matter, ranging from a bit trickier than you might
> think
> > to requiring many man-hours. For the example below, the process could be
> > automated with 99%+ accuracy. I don't know of any off hand, but there are
> > probably sequences in the database whose first non-prime member comes
> quite
> > late. The process also has to be able to deal with sequences having very
> > large terms. One keyword I have considered, "fact", for those sequences
> > which depend on factorization, in the same way that "base" sequences
> depend
> > on representation as numerals, would be very difficult to get anywhere
> > close to being right.
> >
> > Franklin T. Adams-Watters
> >
> >
> > -----Original Message-----
> > From: Felix Fr?hlich <felix.froe at googlemail.com>
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Sent: Fri, Feb 20, 2015 5:10 am
> > Subject: [seqfan] Additional keywords for OEIS
> >
> >
> > Dear SeqFans,
> >
> > as some of you might know, there has been some discussion about the
> > addition of additional keywords to the OEIS. Most of what I found
> regarding
> > that discussion has taken place in the userspace of Charles Greathouse in
> > the OEIS Wiki. See
> > https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> > https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and
> the
> > corresponding talk pages.
> >
> > Personally I think the possibility to refine OEIS searches via specific
> > keywords is very useful and I often make use of that feature. The
> addition
> > of new keywords would allow one to get even more relevant results. For
> > example, Alex Ratushnyak in 2013 suggested the addition of a keyword
> 'prim'
> > that would allow one to find all sequences where all terms are prime. Two
> > obvious candidates for this keyword would be sequences like A000040
> > or A000043.
> >
> > As I am not familiar with the technical aspects behind the OEIS
> database, I
> > would like to know how much work it would be to add new keywords to the
> > OEIS or whether it is technically possible at all (maybe it's just like
> > running an SQL query to update some database table, or maybe it requires
> > some complete rewrite of some part of the software underlying the OEIS, I
> > do not know). If it is technically feasible to do this and if those who
> > maintain the technical integrity of the OEIS think such a step would be
> > desirable, then as a next step we could collect suggestions regarding
> which
> > keywords would be useful.
> >
> > What do others think?
> >
> > Best regards
> >
> > Felix Fr?hlich
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From charles.greathouse at case.edu  Fri Feb 20 23:24:17 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Fri, 20 Feb 2015 17:24:17 -0500
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <241484269.320541.1424426022835.JavaMail.yahoo@mail.yahoo.com>
References: <241484269.320541.1424426022835.JavaMail.yahoo@mail.yahoo.com>
Message-ID: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>

I suspect that there is some k > 1 such that the ratio is greater than k
infinitely often. Is anyone interested in crunching the numbers here on the
heuristic?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <reddwarf2956 at yahoo.com>
wrote:

> Below is a proof based on A005250(n ) of the OEIS.  Can someone look at it
> and tell me if it true?
>
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> If it is true, an edit of A005250 comments is needed.
>
> Related:
>
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
>
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
>
>
>  John W. Nicholson
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From reddwarf2956 at yahoo.com  Sat Feb 21 01:58:06 2015
From: reddwarf2956 at yahoo.com (John W. Nicholson)
Date: Sat, 21 Feb 2015 00:58:06 +0000 (UTC)
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>
References: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>
Message-ID: <422736994.5533162.1424480286641.JavaMail.yahoo@mail.yahoo.com>

Charles, 

Does that mean that the proof with first question, that the ratio <=2, is correct and with out problems so that you are now looking at the second question with the limit of the ratio going to infinity =1??John W. Nicholson 

     On Friday, February 20, 2015 4:24 PM, Charles Greathouse <charles.greathouse at case.edu> wrote:
   
 

 I suspect that there is some k > 1 such that the ratio is greater than k
infinitely often. Is anyone interested in crunching the numbers here on the
heuristic?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <reddwarf2956 at yahoo.com>
wrote:

> Below is a proof based on A005250(n ) of the OEIS.? Can someone look at it
> and tell me if it true?
>
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> If it is true, an edit of A005250 comments is needed.
>
> Related:
>
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
>
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
>
>
>? John W. Nicholson
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


 
   


From seqfan at matcos.nl  Fri Feb 20 21:59:05 2015
From: seqfan at matcos.nl (Matthijs Coster)
Date: Fri, 20 Feb 2015 21:59:05 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
Message-ID: <54E7A019.2050006@matcos.nl>

I would like keywords such that only sequences can be searched which are 
increasing, non decreasing, consist of different integers. That would be 
wonderful!

Matthijs Coster

Charles Greathouse schreef op 20-2-2015 om 20:47:
> I like the idea of new keywords, and I like the idea of categories.
> Categories seem like a great solution to many problems because they would
> be (by design) extendable. Unfortunately I haven't had time to look though
> this part of Russ' code, but I intend to work on this eventually.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 12:24 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
>> Instead of adding more keywords, which are necessarily
>> rather limited, Charles and I had discussed adding
>> "categories".  This may be a better way to proceed.
>> Charles, did you think any more about how this idea might be implemented?
>> IIRC, you started to learn Go for that purpose?
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <
>> franktaw at netscape.net>
>> wrote:
>>
>>> While I'm not familiar with the code being used, making new keywords
>>> available can't be very difficult.
>>>
>>> Getting the keyword assigned to all and only those sequences where it
>>> belongs is another matter, ranging from a bit trickier than you might
>> think
>>> to requiring many man-hours. For the example below, the process could be
>>> automated with 99%+ accuracy. I don't know of any off hand, but there are
>>> probably sequences in the database whose first non-prime member comes
>> quite
>>> late. The process also has to be able to deal with sequences having very
>>> large terms. One keyword I have considered, "fact", for those sequences
>>> which depend on factorization, in the same way that "base" sequences
>> depend
>>> on representation as numerals, would be very difficult to get anywhere
>>> close to being right.
>>>
>>> Franklin T. Adams-Watters
>>>
>>>
>>> -----Original Message-----
>>> From: Felix Fr?hlich <felix.froe at googlemail.com>
>>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> Sent: Fri, Feb 20, 2015 5:10 am
>>> Subject: [seqfan] Additional keywords for OEIS
>>>
>>>
>>> Dear SeqFans,
>>>
>>> as some of you might know, there has been some discussion about the
>>> addition of additional keywords to the OEIS. Most of what I found
>> regarding
>>> that discussion has taken place in the userspace of Charles Greathouse in
>>> the OEIS Wiki. See
>>> https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
>>> https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and
>> the
>>> corresponding talk pages.
>>>
>>> Personally I think the possibility to refine OEIS searches via specific
>>> keywords is very useful and I often make use of that feature. The
>> addition
>>> of new keywords would allow one to get even more relevant results. For
>>> example, Alex Ratushnyak in 2013 suggested the addition of a keyword
>> 'prim'
>>> that would allow one to find all sequences where all terms are prime. Two
>>> obvious candidates for this keyword would be sequences like A000040
>>> or A000043.
>>>
>>> As I am not familiar with the technical aspects behind the OEIS
>> database, I
>>> would like to know how much work it would be to add new keywords to the
>>> OEIS or whether it is technically possible at all (maybe it's just like
>>> running an SQL query to update some database table, or maybe it requires
>>> some complete rewrite of some part of the software underlying the OEIS, I
>>> do not know). If it is technically feasible to do this and if those who
>>> maintain the technical integrity of the OEIS think such a step would be
>>> desirable, then as a next step we could collect suggestions regarding
>> which
>>> keywords would be useful.
>>>
>>> What do others think?
>>>
>>> Best regards
>>>
>>> Felix Fr?hlich
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



From franktaw at netscape.net  Sat Feb 21 08:33:05 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Sat, 21 Feb 2015 02:33:05 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
Message-ID: <8D21BBFC3FD21B5-1B58-8EB7A@webmail-va170.sysops.aol.com>

I don't know what you mean by categories. Is there a reference to this 
in the Wiki?

Franklin T. Adams-Watters

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Feb 20, 2015 1:48 pm
Subject: [seqfan] Re: Additional keywords for OEIS


I like the idea of new keywords, and I like the idea of categories.
Categories seem like a great solution to many problems because they 
would
be (by design) extendable. Unfortunately I haven't had time to look 
though
this part of Russ' code, but I intend to work on this eventually.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 12:24 PM, Neil Sloane <njasloane at gmail.com> 
wrote:

> Instead of adding more keywords, which are necessarily
> rather limited, Charles and I had discussed adding
> "categories".  This may be a better way to proceed.
> Charles, did you think any more about how this idea might be 
implemented?
> IIRC, you started to learn Go for that purpose?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <
> franktaw at netscape.net>
> wrote:
>
> > While I'm not familiar with the code being used, making new keywords
> > available can't be very difficult.
> >
> > Getting the keyword assigned to all and only those sequences where 
it
> > belongs is another matter, ranging from a bit trickier than you 
might
> think
> > to requiring many man-hours. For the example below, the process 
could be
> > automated with 99%+ accuracy. I don't know of any off hand, but 
there are
> > probably sequences in the database whose first non-prime member 
comes
> quite
> > late. The process also has to be able to deal with sequences having 
very
> > large terms. One keyword I have considered, "fact", for those 
sequences
> > which depend on factorization, in the same way that "base" sequences
> depend
> > on representation as numerals, would be very difficult to get 
anywhere
> > close to being right.
> >
> > Franklin T. Adams-Watters
> >
> >
> > -----Original Message-----
> > From: Felix Fr?hlich <felix.froe at googlemail.com>
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Sent: Fri, Feb 20, 2015 5:10 am
> > Subject: [seqfan] Additional keywords for OEIS
> >
> >
> > Dear SeqFans,
> >
> > as some of you might know, there has been some discussion about the
> > addition of additional keywords to the OEIS. Most of what I found
> regarding
> > that discussion has taken place in the userspace of Charles 
Greathouse in
> > the OEIS Wiki. See
> > https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> > https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table 
and
> the
> > corresponding talk pages.
> >
> > Personally I think the possibility to refine OEIS searches via 
specific
> > keywords is very useful and I often make use of that feature. The
> addition
> > of new keywords would allow one to get even more relevant results. 
For
> > example, Alex Ratushnyak in 2013 suggested the addition of a keyword
> 'prim'
> > that would allow one to find all sequences where all terms are 
prime. Two
> > obvious candidates for this keyword would be sequences like A000040
> > or A000043.
> >
> > As I am not familiar with the technical aspects behind the OEIS
> database, I
> > would like to know how much work it would be to add new keywords to 
the
> > OEIS or whether it is technically possible at all (maybe it's just 
like
> > running an SQL query to update some database table, or maybe it 
requires
> > some complete rewrite of some part of the software underlying the 
OEIS, I
> > do not know). If it is technically feasible to do this and if those 
who
> > maintain the technical integrity of the OEIS think such a step 
would be
> > desirable, then as a next step we could collect suggestions 
regarding
> which
> > keywords would be useful.
> >
> > What do others think?
> >
> > Best regards
> >
> > Felix Fr?hlich
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From felix.froe at googlemail.com  Sat Feb 21 09:08:53 2015
From: felix.froe at googlemail.com (=?UTF-8?Q?Felix_Fr=C3=B6hlich?=)
Date: Sat, 21 Feb 2015 09:08:53 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <8D21BBFC3FD21B5-1B58-8EB7A@webmail-va170.sysops.aol.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
 <8D21BBFC3FD21B5-1B58-8EB7A@webmail-va170.sysops.aol.com>
Message-ID: <CAGtmjtQBAsABRZ91VUACbMc4Z2yUfMB=c26vgEDSEqDwV-tdew@mail.gmail.com>

I don't think there is a reference in the OEIS wiki, but for a general
overview of what I believe Neil is referring to above, see
http://www.mediawiki.org/wiki/Help:Categories.

Felix

2015-02-21 8:33 GMT+01:00 Frank Adams-Watters <franktaw at netscape.net>:

> I don't know what you mean by categories. Is there a reference to this in
> the Wiki?
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Charles Greathouse <charles.greathouse at case.edu>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Feb 20, 2015 1:48 pm
> Subject: [seqfan] Re: Additional keywords for OEIS
>
>
> I like the idea of new keywords, and I like the idea of categories.
> Categories seem like a great solution to many problems because they would
> be (by design) extendable. Unfortunately I haven't had time to look though
> this part of Russ' code, but I intend to work on this eventually.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 12:24 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
>  Instead of adding more keywords, which are necessarily
>> rather limited, Charles and I had discussed adding
>> "categories".  This may be a better way to proceed.
>> Charles, did you think any more about how this idea might be
>>
> implemented?
>
>> IIRC, you started to learn Go for that purpose?
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
>>
> NJ.
>
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <
>> franktaw at netscape.net>
>> wrote:
>>
>> > While I'm not familiar with the code being used, making new keywords
>> > available can't be very difficult.
>> >
>> > Getting the keyword assigned to all and only those sequences where
>>
> it
>
>> > belongs is another matter, ranging from a bit trickier than you
>>
> might
>
>> think
>> > to requiring many man-hours. For the example below, the process
>>
> could be
>
>> > automated with 99%+ accuracy. I don't know of any off hand, but
>>
> there are
>
>> > probably sequences in the database whose first non-prime member
>>
> comes
>
>> quite
>> > late. The process also has to be able to deal with sequences having
>>
> very
>
>> > large terms. One keyword I have considered, "fact", for those
>>
> sequences
>
>> > which depend on factorization, in the same way that "base" sequences
>> depend
>> > on representation as numerals, would be very difficult to get
>>
> anywhere
>
>> > close to being right.
>> >
>> > Franklin T. Adams-Watters
>> >
>> >
>> > -----Original Message-----
>> > From: Felix Fr?hlich <felix.froe at googlemail.com>
>> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > Sent: Fri, Feb 20, 2015 5:10 am
>> > Subject: [seqfan] Additional keywords for OEIS
>> >
>> >
>> > Dear SeqFans,
>> >
>> > as some of you might know, there has been some discussion about the
>> > addition of additional keywords to the OEIS. Most of what I found
>> regarding
>> > that discussion has taken place in the userspace of Charles
>>
> Greathouse in
>
>> > the OEIS Wiki. See
>> > https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
>> > https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table
>>
> and
>
>> the
>> > corresponding talk pages.
>> >
>> > Personally I think the possibility to refine OEIS searches via
>>
> specific
>
>> > keywords is very useful and I often make use of that feature. The
>> addition
>> > of new keywords would allow one to get even more relevant results.
>>
> For
>
>> > example, Alex Ratushnyak in 2013 suggested the addition of a keyword
>> 'prim'
>> > that would allow one to find all sequences where all terms are
>>
> prime. Two
>
>> > obvious candidates for this keyword would be sequences like A000040
>> > or A000043.
>> >
>> > As I am not familiar with the technical aspects behind the OEIS
>> database, I
>> > would like to know how much work it would be to add new keywords to
>>
> the
>
>> > OEIS or whether it is technically possible at all (maybe it's just
>>
> like
>
>> > running an SQL query to update some database table, or maybe it
>>
> requires
>
>> > some complete rewrite of some part of the software underlying the
>>
> OEIS, I
>
>> > do not know). If it is technically feasible to do this and if those
>>
> who
>
>> > maintain the technical integrity of the OEIS think such a step
>>
> would be
>
>> > desirable, then as a next step we could collect suggestions
>>
> regarding
>
>> which
>> > keywords would be useful.
>> >
>> > What do others think?
>> >
>> > Best regards
>> >
>> > Felix Fr?hlich
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>> >
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From zbi74583.boat at orange.zero.jp  Sat Feb 21 08:19:14 2015
From: zbi74583.boat at orange.zero.jp (zbi74583.boat at orange.zero.jp)
Date: Sat, 21 Feb 2015 16:19:14 +0900 (JST)
Subject: [seqfan] Re: Generalized Amicable Number
Message-ID: <62970.111.188.22.63.1424503154.squirrel@webmail.zero.jp>

    Hi,Jack
    Thank you for confirming and computing more terms

    The first number was the following

    x = 5^3*11^2*13*131*2^2*3^2
    y = 5^3*11^2*13*131*7^2

    I am sorry that I wrote a wrong number which I wrote on next line in my note
book
    Could you confirm it?



    I am now computing the numbers which satisfy the following

    F(x)=F(y)=m/n*(x*y)^(1/2)

    Where F(k) is one of the divisor function, both m,n are small

    Here is an interesting example

    UnitaryPhi(x)=UnitaryPhi(y)=m/n*(x*y)^(1/2)

    m/n=3/4    A143649
    x = 2^10*5*3^2*11^2
    y = 2^10*5*31^2
    Is it tenth term?

    m/n=4/5
    x = y = 5

    x = 2^2*3^2
    y = 5^2

    x = 5^4*7*2^10*3^8*11^2*41^2
    y = 5^4*7*2^20*3^2*13^2*31^2

    Could you confirm them and compute more terms?



    >(-1)Sigma(x)=(-1)Sigma(y)=8/5*(x*y)^(1/2)

    >The definition of (-1)Sigma(x) is here A049060



    Yasutoshi




From charles.greathouse at case.edu  Sat Feb 21 16:42:35 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Sat, 21 Feb 2015 10:42:35 -0500
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <422736994.5533162.1424480286641.JavaMail.yahoo@mail.yahoo.com>
References: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>
 <422736994.5533162.1424480286641.JavaMail.yahoo@mail.yahoo.com>
Message-ID: <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>

I don't know what to think of the first question. It's numerically
unassailable -- to build up evidence in the primes, one way or another,
you'd probably need to get a lot closer to a googolplex than a googol, and
even 10^20 is out of reach at the moment. The only recourse I see is
checking whether it holds in the Cramer model, flawed as it is.

It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
also wouldn't surprise me if it happened only finitely often.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com>
wrote:

> Charles,
>
> Does that mean that the proof with first question, that the ratio <=2, is
> correct and with out problems so that you are now looking at the second
> question with the limit of the ratio going to infinity =1? John W. Nicholson
>
>      On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>
>
>  I suspect that there is some k > 1 such that the ratio is greater than k
> infinitely often. Is anyone interested in crunching the numbers here on the
> heuristic?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Below is a proof based on A005250(n ) of the OEIS.  Can someone look at
> it
> > and tell me if it true?
> >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > If it is true, an edit of A005250 comments is needed.
> >
> > Related:
> >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> >
> >
> >  John W. Nicholson
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From reddwarf2956 at yahoo.com  Sat Feb 21 19:05:18 2015
From: reddwarf2956 at yahoo.com (John W. Nicholson)
Date: Sat, 21 Feb 2015 18:05:18 +0000 (UTC)
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>
References: <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>
Message-ID: <1727707214.931670.1424541918410.JavaMail.yahoo@mail.yahoo.com>

"It's numerically unassailable"? Please, do explain, because I do not see how it is a problem when I used Ramanujan primes, the RPC, and subsutution to limit the size of the gaps. I don't see how this is different for a large maximal gap too.
?John W. Nicholson 

     On Saturday, February 21, 2015 9:43 AM, Charles Greathouse <charles.greathouse at case.edu> wrote:
   
 

 I don't know what to think of the first question. It's numerically
unassailable -- to build up evidence in the primes, one way or another,
you'd probably need to get a lot closer to a googolplex than a googol, and
even 10^20 is out of reach at the moment. The only recourse I see is
checking whether it holds in the Cramer model, flawed as it is.

It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
also wouldn't surprise me if it happened only finitely often.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com>
wrote:

> Charles,
>
> Does that mean that the proof with first question, that the ratio <=2, is
> correct and with out problems so that you are now looking at the second
> question with the limit of the ratio going to infinity =1? John W. Nicholson
>
>? ? ? On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>
>
>? I suspect that there is some k > 1 such that the ratio is greater than k
> infinitely often. Is anyone interested in crunching the numbers here on the
> heuristic?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Below is a proof based on A005250(n ) of the OEIS.? Can someone look at
> it
> > and tell me if it true?
> >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > If it is true, an edit of A005250 comments is needed.
> >
> > Related:
> >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> >
> >
> >? John W. Nicholson
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


 
   


From zbi74583.boat at orange.zero.jp  Sat Feb 21 08:28:54 2015
From: zbi74583.boat at orange.zero.jp (zbi74583.boat at orange.zero.jp)
Date: Sat, 21 Feb 2015 16:28:54 +0900 (JST)
Subject: [seqfan] Song of Integer
Message-ID: <62987.111.188.22.63.1424503734.squirrel@webmail.zero.jp>

    Hi,Seqfans

    Do you know "BABYMETAL" who is a girl  matal band?
    Their album got top of World Albums in Billboard of USA
    "Megitsune"

    https://www.youtube.com/watch?v=cK3NMZAUKGw

    They also sing a song of "Integer"
    "4 No Uta" which means "Song of four"
    Live in London

    https://www.youtube.com/watch?v=chYaUGOTo3I

    Lylic of the song

    https://www.youtube.com/watch?v=ASyqaP6dguA

    Two younger members of them wrote it when they were twelve years old
    I think they are so smart



    Yasutoshi




From olivier.gerard at gmail.com  Sun Feb 22 00:51:07 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Sun, 22 Feb 2015 00:51:07 +0100
Subject: [seqfan] Fwd : House of Graphs: a database of interesting graphs --
	an update
Message-ID: <CAAcpPSZ5vW1BJrRGYittRnqMDHt=o74TjJoqXiSzvj33d=PCLg@mail.gmail.com>

This might be of interest to several seqfan members.

With my best regards,

Olivier G?rard



---------- Forwarded message ----------
From: Jan Goedgebeur <jan.goedgebeur at ugent.be>
Date: Tue, Feb 17, 2015 at 2:46 PM


Already in 2012 we announced the website "House of Graphs" --
http://hog.grinvin.org/ . In the meantime several new lists of graphs,
"interesting graphs", and invariants have been added to the website.

"House of Graphs" hosts lists of graphs (like Snarks, Fullerenes, etc.) and
links to other pages with lists of combinatorial structures (like vertex
transitive graphs, Ramsey graphs, etc.). But its main feature is a
searchable database of graphs that already occurred as counterexamples to
conjectures, as extremal graphs or in other contexts. In short we call this
the database of "interesting graphs".

The key idea is that although already for small vertex numbers extremely
many graphs exist, there are some that serve again and again as
counterexamples and that a database of these graphs should be established.
In this database one can e.g. search for graphs with certain invariant
values, graphs with a certain name (e.g. Petersen, Heawood, Balaban, etc.)
or graphs that are marked as being interesting for a certain invariant
(e.g. marked as being interesting for the girth). These searches can of
course also be combined and the results downloaded so that one gets good
candidates for testing new conjectures one is working on.

Users can also add graphs to the database. If the graphs are not yet in the
database, the system computes invariant values for the graphs. So the
database can also be used as a repository. If you discover new interesting
graphs, you can make them available to other users by submitting them to
the database together with a text identifier (e.g.
counterexample_this_conjecture).
Then other scientists can find and download the graph from "House of
Graphs".

More information on "House of Graphs" and its functionalities is given in:

Discrete Applied Mathematics, Volume 161, Issues 1-2, Jan. 2013, pages
311-314
Available online: http://dx.doi.org/10.1016/j.dam.2012.07.018

and

http://arxiv.org/abs/1204.3549

while "House of Graphs" can be accessed at: http://hog.grinvin.org/


Gunnar Brinkmann, Kris Coolsaet, Jan Goedgebeur and Hadrien Melot

-- 

Jan Goedgebeur
Applied Mathematics and Computer Science
Ghent University
Krijgslaan 281 - S9
B - 9000 Ghent


From pew at worldwidemann.com  Sun Feb 22 22:29:17 2015
From: pew at worldwidemann.com (Philipp Emanuel Weidmann)
Date: Sun, 22 Feb 2015 22:29:17 +0100
Subject: [seqfan] Purely algorithmic number sequence identification
Message-ID: <1424640557.3507.31.camel@worldwidemann.com>

I have been experimenting with a purely algorithmic (brute force)
approach to the question "which formula generates this number
sequence?", designed to complement existing systems based on database
lookups (OEIS) and pattern transforms (Mathematica).

The system developed for that purpose is now available, both as a
library/executable JAR (https://github.com/p-e-w/sequencer) and as a
simple (beta stage) web service (http://www.sequenceboss.org/).

At its core, Sequencer is a tree-based expression generator plus a
hybrid search engine combining a fast numerical pre-checker with a
symbolic verifier. Because the numerical checker is so fast, expressions
of relatively high complexity (7-8 nodes) can be exhaustively searched
in minutes on commodity hardware to check whether they generate the
given numbers.

Despite its early stage of development, Sequencer can already identify
(i.e. find a closed form expression for) many sequences that OEIS,
Superseeker and Mathematica can not. It is particularly strong at
finding complex, nonlinear or inhomogeneous recurrence relations like

  a(1) = 1
  a(2) = 1
  a(3) = 1
  a(n) = a(n-2)^2+a(n-1)+a(n-3)   for n >= 4

when provided the sequence

  1, 1, 1, 3, 5, 15, 43, 273

something which none of the above mentioned systems is currently able to
do. But the system can also quickly find unusual, relatively simple
general terms for sequences like

  11, 47, 123, 214, 257

for which Sequencer returns

  a(n) = n + Binomial(10,n)

in less than one second (http://www.sequenceboss.org/?q=11%2C+47%2C+123%
2C+214%2C+257).

By leveraging the Symja computer algebra system, Sequencer supports
fully symbolic input and output and is not limited to integer sequences.
For example, running the program on the input

  0, 1/2, sqrt(3)/2, 1

produces (search depth 6) the formula

  a(n) = Sin(1/6*Pi*(n-1))


I invite you to give the Sequencer/SequenceBoss system a try. If you are
familiar with Scala, you will find it easy to modify the
FormulaGenerator class to expand the range of expressions that can be
searched beyond what the command line switches already offer. Next in
line I plan to add multicore support based on Scala Actors which should
almost multiply the current search performance by the number of
available CPU cores as the search is efficiently parallelizable. Bug
reports and code contributions are very welcome, ideally on GitHub.

Best regards

Philipp Emanuel Weidmann




From akourbatov at gmail.com  Sun Feb 22 23:04:10 2015
From: akourbatov at gmail.com (Alexei Kourbatov)
Date: Sun, 22 Feb 2015 14:04:10 -0800
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>
References: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>
 <422736994.5533162.1424480286641.JavaMail.yahoo@mail.yahoo.com>
 <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>
Message-ID: <CAE3sB-CuevC0dyw7c-uut2NVDBdbCuKRj2uyS74GdST0uR=MVw@mail.gmail.com>

In Cramer's model, I feel that both statements are true with probability 1.

In the original proof, the last sentence "So the gap g_y ..." apparently
does not follow from the preceding statements (as far as I can tell).
To illustrate my point: a-c < 2(b-d) does not follow from { a < 2b and c <
2d} - but it would follow e.g. from { a < 2b and c >= 2d}



On Sat, Feb 21, 2015 at 7:42 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> I don't know what to think of the first question. It's numerically
> unassailable -- to build up evidence in the primes, one way or another,
> you'd probably need to get a lot closer to a googolplex than a googol, and
> even 10^20 is out of reach at the moment. The only recourse I see is
> checking whether it holds in the Cramer model, flawed as it is.
>
> It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
> also wouldn't surprise me if it happened only finitely often.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Charles,
> >
> > Does that mean that the proof with first question, that the ratio <=2, is
> > correct and with out problems so that you are now looking at the second
> > question with the limit of the ratio going to infinity =1? John W.
> Nicholson
> >
> >      On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> > charles.greathouse at case.edu> wrote:
> >
> >
> >
> >  I suspect that there is some k > 1 such that the ratio is greater than k
> > infinitely often. Is anyone interested in crunching the numbers here on
> the
> > heuristic?
> >
> > Charles Greathouse
> > Analyst/Programmer
> > Case Western Reserve University
> >
> > On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <
> reddwarf2956 at yahoo.com
> > >
> > wrote:
> >
> > > Below is a proof based on A005250(n ) of the OEIS.  Can someone look at
> > it
> > > and tell me if it true?
> > >
> > >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > > If it is true, an edit of A005250 comments is needed.
> > >
> > > Related:
> > >
> > >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> > >
> > >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> > >
> > >
> > >  John W. Nicholson
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From olivier.gerard at gmail.com  Mon Feb 23 11:42:45 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Mon, 23 Feb 2015 11:42:45 +0100
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <1424640557.3507.31.camel@worldwidemann.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
Message-ID: <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>

Dear Philipp Emmanuel,

your program Sequencer is really interesting. In spirit, one can say it is
close to
Robert Munafo's RIES

http://mrob.com/pub/ries/index.html

but for integer sequences

It would be nice to test it on "hard" sequences and other sequences without
formula.

I have a first candidate (which is inspired by the same kind of brute force
exploration)

https://oeis.org/A229673

"The number of subsets of nonzero integers of cardinality n, produced as
the steps in a computation starting with 1 and using the operations of
multiplication, addition, or subtraction."

1, 3, 15, 126, 1667, 31966, 828678, 27535826, 1128945382, ...

Best regards,

Olivier


On Sun, Feb 22, 2015 at 10:29 PM, Philipp Emanuel Weidmann <
pew at worldwidemann.com> wrote:

> I have been experimenting with a purely algorithmic (brute force)
> approach to the question "which formula generates this number
> sequence?", designed to complement existing systems based on database
> lookups (OEIS) and pattern transforms (Mathematica).
>
>
Mathematica has pattern transforms as part of its language but its sequence
formula recognition commands are based on mathematical theories :

 - holonomic functions, linear algebra, z-transforms, difference equations,
continuous fractions, pade approximants, ...



> The system developed for that purpose is now available, both as a
> library/executable JAR (https://github.com/p-e-w/sequencer) and as a
> simple (beta stage) web service (http://www.sequenceboss.org/).
>
> At its core, Sequencer is a tree-based expression generator plus a
> hybrid search engine combining a fast numerical pre-checker with a
> symbolic verifier. Because the numerical checker is so fast, expressions
> of relatively high complexity (7-8 nodes) can be exhaustively searched
> in minutes on commodity hardware to check whether they generate the
> given numbers.
>
> Despite its early stage of development, Sequencer can already identify
> (i.e. find a closed form expression for) many sequences that OEIS,
> Superseeker and Mathematica can not. It is particularly strong at
> finding complex, nonlinear or inhomogeneous recurrence relations like
>
>   a(1) = 1
>   a(2) = 1
>   a(3) = 1
>   a(n) = a(n-2)^2+a(n-1)+a(n-3)   for n >= 4
>
> when provided the sequence
>
>   1, 1, 1, 3, 5, 15, 43, 273
>
> something which none of the above mentioned systems is currently able to
> do. But the system can also quickly find unusual, relatively simple
> general terms for sequences like
>
>   11, 47, 123, 214, 257
>
> for which Sequencer returns
>
>   a(n) = n + Binomial(10,n)
>
> in less than one second (http://www.sequenceboss.org/?q=11%2C+47%2C+123%
> 2C+214%2C+257).
>
> By leveraging the Symja computer algebra system, Sequencer supports
> fully symbolic input and output and is not limited to integer sequences.
> For example, running the program on the input
>
>   0, 1/2, sqrt(3)/2, 1
>
> produces (search depth 6) the formula
>
>   a(n) = Sin(1/6*Pi*(n-1))
>
>
> I invite you to give the Sequencer/SequenceBoss system a try. If you are
> familiar with Scala, you will find it easy to modify the
> FormulaGenerator class to expand the range of expressions that can be
> searched beyond what the command line switches already offer. Next in
> line I plan to add multicore support based on Scala Actors which should
> almost multiply the current search performance by the number of
> available CPU cores as the search is efficiently parallelizable. Bug
> reports and code contributions are very welcome, ideally on GitHub.
>
> Best regards
>
> Philipp Emanuel Weidmann
>


From wclark at mail.usf.edu  Mon Feb 23 17:02:37 2015
From: wclark at mail.usf.edu (W. Edwin Clark)
Date: Mon, 23 Feb 2015 11:02:37 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
Message-ID: <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>

On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <olivier.gerard at gmail.com>
wrote:

>
> It would be nice to test it on "hard" sequences and other sequences without
> formula.
>
>
>
For example:  http://oeis.org/A000001, the number of groups of order n :-)

Or perhaps easier:  http://oeis.org/A000688, the number of abelian groups
of order n.


From mlb at well.com  Mon Feb 23 22:02:26 2015
From: mlb at well.com (Marc LeBrun)
Date: Mon, 23 Feb 2015 13:02:26 -0800
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
Message-ID: <D110D562.19B0B%mlb@well.com>

It is my fond and enduring hope that the OEIS will someday enjoy the same
level of sophistication in its data science content as it does in its
mathematical content.

Features such as ad hoc keywords or categories are innocuous insofar as they
go, and useful within their scope, but they seem pretty primitive compared
to the current state-of-the-art in data modeling and knowledge engineering.

I recommend that anyone with an interest in these proposals with an eye
towards the future of the OEIS should look into things like the semantic web
to get a more up-to-date appreciation for where such technologies are going
(indeed, have already gone).

For example a keyword can be viewed as metadata that makes an assertion
*about a sequence*.  But instead of having "?" variants of every keyword one
can instead have a general kind of "meta" assertion *about an assertion*
that says it is conjectural.  And so on for many other applications (eg
assertions for provenance attribution, processing inferential consequences
of keywords such as prim==>nonn, etc etc).

The point is that there already exist sophisticated and elegant data
languages for representing this kind of information.  The OEIS should
consider adopting these approaches, rather than reinventing the wheel.

But heck, even if we just go ahead and kludge stuff up the good news is that
the total amount of actual data in the OEIS is truly miniscule by modern
standards.  This relative footprint will continue to shrink, at least while
the primary source of content continues to be entries hand-crafted by human
beings.  This means that building and maintaining useful informational
superstructures around the OEIS will lie well within the scope of
contemporary tools and techniques, and they can flourish off-site if not on.

With the current commercial interest around "big data" in many forms and its
consequent stimulation of academia, maybe we could get, say, a coven of grad
students to take a hands-on interest in this important aspect of the OEIS
and help us cook up something more au courant?




From mathar at mpia-hd.mpg.de  Mon Feb 23 23:21:39 2015
From: mathar at mpia-hd.mpg.de (Richard J. Mathar)
Date: Mon, 23 Feb 2015 23:21:39 +0100
Subject: [seqfan] Q on g.f. A138164
Message-ID: <20150223222139.GA13412@mathar.mpia-hd.mpg.de>

Is the generating function in http://oeis.org/A138164 correct?
The Maple implementation

vx := 2/sqrt(3)*sin(sin(x*3*sqrt(3)/2)/3) ;
A138164 := proc(n)
        1/(1-vx-vx^2) ;
        coeftayl(%,x=0,n) ;
end proc:
seq(%(n),n=0..13) ;

generates fractions from the power(x^3) on.


From pauldhanna at juno.com  Tue Feb 24 00:41:24 2015
From: pauldhanna at juno.com (Paul D Hanna)
Date: Mon, 23 Feb 2015 23:41:24 GMT
Subject: [seqfan] Re: Q on g.f. A138164
Message-ID: <20150223.184124.23772.0@webmail01.dca.untd.com>

Richard, 
     Good catch.  The formula should read: 
  
"G.f.: 1/(1-v-v^2) where v=(2/sqrt(3))*sin(arcsin(x*3*sqrt(3)/2)/3) is the series reversion of x*(1-x^2); ..."
 
(i.e., the second 'sin' should be 'arcsin') 
and a reference to A001764 would be in order since 
v = Sum_{n>=1} A001764(n-1)*x^(2*n-1). 
    Paul 
 
---------- Original Message ----------
From: "Richard J. Mathar" <mathar at mpia-hd.mpg.de>
To: seqfan at seqfan.eu
Subject: [seqfan] Q on g.f. A138164
Date: Mon, 23 Feb 2015 23:21:39 +0100

Is the generating function in http://oeis.org/A138164 correct?
The Maple implementation

vx := 2/sqrt(3)*sin(sin(x*3*sqrt(3)/2)/3) ;
A138164 := proc(n)
        1/(1-vx-vx^2) ;
        coeftayl(%,x=0,n) ;
end proc:
seq(%(n),n=0..13) ;

generates fractions from the power(x^3) on.

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/



From arndt at jjj.de  Tue Feb 24 08:56:40 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Tue, 24 Feb 2015 08:56:40 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <D110D562.19B0B%mlb@well.com>
References: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <D110D562.19B0B%mlb@well.com>
Message-ID: <20150224075640.GA1671@jjj.de>

* Marc LeBrun <mlb at well.com> [Feb 24. 2015 08:40]:
> It is my fond and enduring hope that the OEIS will someday enjoy the same
> level of sophistication in its data science content as it does in its
> mathematical content.
> 
> [...]
> 
> With the current commercial interest around "big data" in many forms and its
> consequent stimulation of academia, maybe we could get, say, a coven of grad
> students to take a hands-on interest in this important aspect of the OEIS
> and help us cook up something more au courant?
> 
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/

I do agree with all you are saying.

There are plans for a "big data" project involving the OEIS, this is
related to the Zentralblatt-Math project that will hopefully start
soon-ish.  A student of mine is just finishing his thesis about parsing
formulas in the OEIS for the Zentralblatt.

Of course it all depends on the funding.

Best regards,  jj


From njasloane at gmail.com  Tue Feb 24 13:37:00 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 24 Feb 2015 07:37:00 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <20150224075640.GA1671@jjj.de>
References: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <D110D562.19B0B%mlb@well.com> <20150224075640.GA1671@jjj.de>
Message-ID: <CAAOnSgQV3o24CB4JDFCtjvuJw6zNY31RsU8ctypP867==yygUQ@mail.gmail.com>

> Of course it all depends on the funding.

If this becomes a problem, there is always the possibility that
the OEIS Foundation could try to raise some money to
help with the project.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Feb 24, 2015 at 2:56 AM, Joerg Arndt <arndt at jjj.de> wrote:

> * Marc LeBrun <mlb at well.com> [Feb 24. 2015 08:40]:
> > It is my fond and enduring hope that the OEIS will someday enjoy the same
> > level of sophistication in its data science content as it does in its
> > mathematical content.
> >
> > [...]
> >
> > With the current commercial interest around "big data" in many forms and
> its
> > consequent stimulation of academia, maybe we could get, say, a coven of
> grad
> > students to take a hands-on interest in this important aspect of the OEIS
> > and help us cook up something more au courant?
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> I do agree with all you are saying.
>
> There are plans for a "big data" project involving the OEIS, this is
> related to the Zentralblatt-Math project that will hopefully start
> soon-ish.  A student of mine is just finishing his thesis about parsing
> formulas in the OEIS for the Zentralblatt.
>
> Of course it all depends on the funding.
>
> Best regards,  jj
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From reddwarf2956 at yahoo.com  Mon Feb 23 05:04:01 2015
From: reddwarf2956 at yahoo.com (John W. Nicholson)
Date: Mon, 23 Feb 2015 04:04:01 +0000 (UTC)
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <CAE3sB-CuevC0dyw7c-uut2NVDBdbCuKRj2uyS74GdST0uR=MVw@mail.gmail.com>
References: <CAE3sB-CuevC0dyw7c-uut2NVDBdbCuKRj2uyS74GdST0uR=MVw@mail.gmail.com>
Message-ID: <370292300.7299941.1424664241563.JavaMail.yahoo@mail.yahoo.com>

Alexei Kourbatov,
First of all thanks for being clear with your concerns. Second, do remember the note:

"All gaps g_i = p_{i+1} ? p_i, where p_i < p_y are g_i <= G_n(x)."

Maybe I need to add the following:

Under the assumption that the smaller gap is p_{y-b+1} - p_{y-b} = G_n(x), we see that the larger gap is p_{y+1} - p_y <= 2*G_n(x).

Is that OK??John W. Nicholson 

     On Sunday, February 22, 2015 5:17 PM, Alexei Kourbatov <akourbatov at gmail.com> wrote:
   
 

 In Cramer's model, I feel that both statements are true with probability 1.

In the original proof, the last sentence "So the gap g_y ..." apparently
does not follow from the preceding statements (as far as I can tell).
To illustrate my point: a-c < 2(b-d) does not follow from { a < 2b and c <
2d} - but it would follow e.g. from { a < 2b and c >= 2d}



On Sat, Feb 21, 2015 at 7:42 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> I don't know what to think of the first question. It's numerically
> unassailable -- to build up evidence in the primes, one way or another,
> you'd probably need to get a lot closer to a googolplex than a googol, and
> even 10^20 is out of reach at the moment. The only recourse I see is
> checking whether it holds in the Cramer model, flawed as it is.
>
> It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
> also wouldn't surprise me if it happened only finitely often.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Charles,
> >
> > Does that mean that the proof with first question, that the ratio <=2, is
> > correct and with out problems so that you are now looking at the second
> > question with the limit of the ratio going to infinity =1? John W.
> Nicholson
> >
> >? ? ? On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> > charles.greathouse at case.edu> wrote:
> >
> >
> >
> >? I suspect that there is some k > 1 such that the ratio is greater than k
> > infinitely often. Is anyone interested in crunching the numbers here on
> the
> > heuristic?
> >
> > Charles Greathouse
> > Analyst/Programmer
> > Case Western Reserve University
> >
> > On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <
> reddwarf2956 at yahoo.com
> > >
> > wrote:
> >
> > > Below is a proof based on A005250(n ) of the OEIS.? Can someone look at
> > it
> > > and tell me if it true?
> > >
> > >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > > If it is true, an edit of A005250 comments is needed.
> > >
> > > Related:
> > >
> > >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> > >
> > >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> > >
> > >
> > >? John W. Nicholson
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


 
   


From pew at worldwidemann.com  Mon Feb 23 19:21:07 2015
From: pew at worldwidemann.com (Philipp Emanuel Weidmann)
Date: Mon, 23 Feb 2015 19:21:07 +0100
Subject: [seqfan]  Re: Purely algorithmic number sequence identification
In-Reply-To: <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
Message-ID: <1424715667.2631.30.camel@worldwidemann.com>

Well, it turns out the first eight elements of A000001 satisfy the, umm,
"slightly exotic" recurrence relation

  a(1) = 1
  a(2) = 1
  a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3

;)

In earnest, while I doubt that brute forcing formulas will bring any
insight into sequences that have baffled mathematicians for centuries
with their irregularity, what might indeed be interesting is to run the
system not on one sequence, but on tens of thousands, all of which have
no closed-form expression associated with them (is there a way to query
those on OEIS?). In a matter of days, Sequencer would likely return a
hundred or so closed forms, some of which may prove correct, which could
then be investigated rigorously.

For such a search, I should probably also add a lot more combinatorial
and number theoretic primitives to the formula generator ? whenever I
randomly browse around OEIS, most of the sequences seem to be counting
problems of some kind.

Best regards
Philipp




On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <olivier.gerard at gmail.com>
> wrote:
> 
> >
> > It would be nice to test it on "hard" sequences and other sequences without
> > formula.
> >
> >
> >
> For example:  http://oeis.org/A000001, the number of groups of order n :-)
> 
> Or perhaps easier:  http://oeis.org/A000688, the number of abelian groups
> of order n.
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/




From njasloane at gmail.com  Tue Feb 24 14:17:28 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 24 Feb 2015 08:17:28 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <1424715667.2631.30.camel@worldwidemann.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
Message-ID: <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>

What do you think of adding your program to Superseeker?  It sounds like
this would definitely be worth doing.

By the way, can you do anything with A122536?  We have 200 terms, but no
formula or recurrence!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
pew at worldwidemann.com> wrote:

> Well, it turns out the first eight elements of A000001 satisfy the, umm,
> "slightly exotic" recurrence relation
>
>   a(1) = 1
>   a(2) = 1
>   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>
> ;)
>
> In earnest, while I doubt that brute forcing formulas will bring any
> insight into sequences that have baffled mathematicians for centuries
> with their irregularity, what might indeed be interesting is to run the
> system not on one sequence, but on tens of thousands, all of which have
> no closed-form expression associated with them (is there a way to query
> those on OEIS?). In a matter of days, Sequencer would likely return a
> hundred or so closed forms, some of which may prove correct, which could
> then be investigated rigorously.
>
> For such a search, I should probably also add a lot more combinatorial
> and number theoretic primitives to the formula generator ? whenever I
> randomly browse around OEIS, most of the sequences seem to be counting
> problems of some kind.
>
> Best regards
> Philipp
>
>
>
>
> On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
> olivier.gerard at gmail.com>
> > wrote:
> >
> > >
> > > It would be nice to test it on "hard" sequences and other sequences
> without
> > > formula.
> > >
> > >
> > >
> > For example:  http://oeis.org/A000001, the number of groups of order n
> :-)
> >
> > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
> groups
> > of order n.
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From benoit.jubin at gmail.com  Tue Feb 24 17:49:38 2015
From: benoit.jubin at gmail.com (=?UTF-8?Q?Beno=C3=AEt_Jubin?=)
Date: Tue, 24 Feb 2015 17:49:38 +0100
Subject: [seqfan] Improved lower bound for A250000
Message-ID: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>

Dear seqfans,

Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on
an (n,n) chessboard.

By modifying the Pratt--Selcoe configuration, I improved the best known
lower bound from
a(n) > (9/4)*(n/4)^2
to
a(n) > (7/3)*(n/4)^2.
I have been sloppy with side effects, but to be on the safe side, let's say
a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the
coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the
following description.

The configuration in the limit n = infinity is as follows: denoting by x,y
in [0,1] the coordinates on the chessboard, the queens of one color are in
the two regions
x<1/4, y<1/2, x<y<x+1/3
and
1/2<x<3/4, y<x-1/3, y<1-x
and the queens of the other color are obtained by central symmetry. As you
can guess, I obtained these coefficients by equalizing the lengths of the
"opposite" boundaries of the armies (this already improves (by 1) on the
"Board 4" example of the webpage).

Using an easy upper bound, one has asymptotically
(2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
Anyone to help fill the gap?

Best,
Benoit


From Rob.Pratt at sas.com  Tue Feb 24 18:13:26 2015
From: Rob.Pratt at sas.com (Rob Pratt)
Date: Tue, 24 Feb 2015 17:13:26 +0000
Subject: [seqfan] Re: Improved lower bound for A250000
In-Reply-To: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
References: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
Message-ID: <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>

Please share your n =24 solution.  Under the central symmetry constraint, I get a maximum of 80, not 84.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Beno?t Jubin
Sent: Tuesday, February 24, 2015 11:50 AM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Improved lower bound for A250000

Dear seqfans,

Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on an (n,n) chessboard.

By modifying the Pratt--Selcoe configuration, I improved the best known lower bound from
a(n) > (9/4)*(n/4)^2
to
a(n) > (7/3)*(n/4)^2.
I have been sloppy with side effects, but to be on the safe side, let's say
a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the following description.

The configuration in the limit n = infinity is as follows: denoting by x,y in [0,1] the coordinates on the chessboard, the queens of one color are in the two regions x<1/4, y<1/2, x<y<x+1/3 and 1/2<x<3/4, y<x-1/3, y<1-x and the queens of the other color are obtained by central symmetry. As you can guess, I obtained these coefficients by equalizing the lengths of the "opposite" boundaries of the armies (this already improves (by 1) on the "Board 4" example of the webpage).

Using an easy upper bound, one has asymptotically
(2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
Anyone to help fill the gap?

Best,
Benoit

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/

From benoit.jubin at gmail.com  Tue Feb 24 18:25:19 2015
From: benoit.jubin at gmail.com (=?UTF-8?Q?Beno=C3=AEt_Jubin?=)
Date: Tue, 24 Feb 2015 18:25:19 +0100
Subject: [seqfan] Re: Improved lower bound for A250000
In-Reply-To: <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>
References: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
 <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>
Message-ID: <CAEG8PYvDamRCbDj9dfC=cyeLrpYLThJGPZyCqr6QMvvt_wEKUQ@mail.gmail.com>

Dear Rob,
I improved by one the final board on the webpage by using the same idea as
for my asymptotic bound, but you are right that in this specific case, the
result is not centrally symmetric. From the last example on the webpage, I
made marginal changes along the diagonals (in the [0,1]^2 coordinates)
y=x+1/3 (deleted 3 Ws, added 5 Bs) and y=x-1/3 (deleted 4 Bs, added 4Ws):

------------------------

......WWWWWW............

......WWWWWW...........W

......WWWWWW..........WW

......WWWWWW.........WWW

......WWWWWW........WWWW

......WWWWW........WWWWW

.......WWW........WWWWWW

........W.........WWWWWW

..................WWWWWW

..................WWWWW.

..................WWWW..

..................WWW...

....BB..................

...BBB..................

..BBBB..................

.BBBBB..................

BBBBBB..........B.......

BBBBBB.........BBB......

BBBBBB........BBBB......

BBBBB........BBBBB......

BBBB........BBBBBB......

BBB.........BBBBBB......

BB..........BBBBBB......

B...........BBBBBB......

------------------------



On Tue, Feb 24, 2015 at 6:13 PM, Rob Pratt <Rob.Pratt at sas.com> wrote:

> Please share your n =24 solution.  Under the central symmetry constraint,
> I get a maximum of 80, not 84.
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Beno?t
> Jubin
> Sent: Tuesday, February 24, 2015 11:50 AM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Improved lower bound for A250000
>
> Dear seqfans,
>
> Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on
> an (n,n) chessboard.
>
> By modifying the Pratt--Selcoe configuration, I improved the best known
> lower bound from
> a(n) > (9/4)*(n/4)^2
> to
> a(n) > (7/3)*(n/4)^2.
> I have been sloppy with side effects, but to be on the safe side, let's say
> a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the
> coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the
> following description.
>
> The configuration in the limit n = infinity is as follows: denoting by x,y
> in [0,1] the coordinates on the chessboard, the queens of one color are in
> the two regions x<1/4, y<1/2, x<y<x+1/3 and 1/2<x<3/4, y<x-1/3, y<1-x and
> the queens of the other color are obtained by central symmetry. As you can
> guess, I obtained these coefficients by equalizing the lengths of the
> "opposite" boundaries of the armies (this already improves (by 1) on the
> "Board 4" example of the webpage).
>
> Using an easy upper bound, one has asymptotically
> (2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
> Anyone to help fill the gap?
>
> Best,
> Benoit
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From Eric.Angelini at kntv.be  Tue Feb 24 19:13:22 2015
From: Eric.Angelini at kntv.be (Eric Angelini)
Date: Tue, 24 Feb 2015 19:13:22 +0100
Subject: [seqfan] Prime by concatenation
Message-ID: <8B00BFBA136BAB43AD27F9EDC3758F03BD24CA5286@KNTVSRV01.kntv.local>

Hello Seqfans,
Concatenate any two digits of S separated by a comma: 
the resulting 2-digit number is prime.

If we accept that [70,2] produces the prime "2"
(concatenation of 0 and 2), then S is a permutation
of {the positive integers} - {4,6,8,9}:

S = 1,3,7,9,70,2,30,5,31,10,20,21,11,12,32,33,13,14,15,...

As usual, S was extended with the smallest integer
not yet present in S and not leading to a contradiction.

Best,
?.






From pew at worldwidemann.com  Tue Feb 24 21:37:36 2015
From: pew at worldwidemann.com (Philipp Emanuel Weidmann)
Date: Tue, 24 Feb 2015 21:37:36 +0100
Subject: [seqfan]  Re: Purely algorithmic number sequence identification
In-Reply-To: <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
 <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
Message-ID: <1424810256.2771.27.camel@worldwidemann.com>

Sounds good, how would that work? Sequencer already has a public API
(documented at https://github.com/p-e-w/sequencer#api) so integration
should be easy as long as Superseeker has a way to interface with a JVM
library.

As for A122536, nothing so far I'm afraid. I really would like to run a
mass search on sequences without formulas though. Do you perhaps know of
a way to find just those on OEIS? Soon the batch of performance
improvements I'm currently working on will be finished, and then
Sequencer should be able to search all depth 6 formulas for more than
1000 Sequences per day. Also, a batch mode could be implemented, which
would allow the program to process a large number of sequences at once,
dramatically improving performance for this use case. Indeed, all of
OEIS could be checked this way in about a week probably ? which would
also be interesting for sequences that already *have* formulas, as some
of them may possess interesting alternative forms, or be incorrect.

Best regards
Philipp





On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
> What do you think of adding your program to Superseeker?  It sounds like
> this would definitely be worth doing.
> 
> By the way, can you do anything with A122536?  We have 200 terms, but no
> formula or recurrence!
> 
> Best regards
> Neil
> 
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
> 
> 
> On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
> pew at worldwidemann.com> wrote:
> 
> > Well, it turns out the first eight elements of A000001 satisfy the, umm,
> > "slightly exotic" recurrence relation
> >
> >   a(1) = 1
> >   a(2) = 1
> >   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
> >
> > ;)
> >
> > In earnest, while I doubt that brute forcing formulas will bring any
> > insight into sequences that have baffled mathematicians for centuries
> > with their irregularity, what might indeed be interesting is to run the
> > system not on one sequence, but on tens of thousands, all of which have
> > no closed-form expression associated with them (is there a way to query
> > those on OEIS?). In a matter of days, Sequencer would likely return a
> > hundred or so closed forms, some of which may prove correct, which could
> > then be investigated rigorously.
> >
> > For such a search, I should probably also add a lot more combinatorial
> > and number theoretic primitives to the formula generator ? whenever I
> > randomly browse around OEIS, most of the sequences seem to be counting
> > problems of some kind.
> >
> > Best regards
> > Philipp
> >
> >
> >
> >
> > On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> > > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
> > olivier.gerard at gmail.com>
> > > wrote:
> > >
> > > >
> > > > It would be nice to test it on "hard" sequences and other sequences
> > without
> > > > formula.
> > > >
> > > >
> > > >
> > > For example:  http://oeis.org/A000001, the number of groups of order n
> > :-)
> > >
> > > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
> > groups
> > > of order n.
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/




From franktaw at netscape.net  Wed Feb 25 00:17:03 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Tue, 24 Feb 2015 18:17:03 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <1424810256.2771.27.camel@worldwidemann.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
 <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
 <1424810256.2771.27.camel@worldwidemann.com>
Message-ID: <8D21E9F22268966-720-A8A7C@webmail-vm046.sysops.aol.com>

If you search in the native format for sequences without "%F" lines, 
you will find the sequences with no formulas present at all. This still 
leaves a larger number of sequences for which some formula has been 
added, but not a formula specifically to define the sequence.

Franklin T. Adams-Watters

-----Original Message-----
From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Tue, Feb 24, 2015 5:09 pm
Subject: [seqfan]  Re: Purely algorithmic number sequence identification


Sounds good, how would that work? Sequencer already has a public API
(documented at https://github.com/p-e-w/sequencer#api) so integration
should be easy as long as Superseeker has a way to interface with a JVM
library.

As for A122536, nothing so far I'm afraid. I really would like to run a
mass search on sequences without formulas though. Do you perhaps know of
a way to find just those on OEIS? Soon the batch of performance
improvements I'm currently working on will be finished, and then
Sequencer should be able to search all depth 6 formulas for more than
1000 Sequences per day. Also, a batch mode could be implemented, which
would allow the program to process a large number of sequences at once,
dramatically improving performance for this use case. Indeed, all of
OEIS could be checked this way in about a week probably ? which would
also be interesting for sequences that already *have* formulas, as some
of them may possess interesting alternative forms, or be incorrect.

Best regards
Philipp





On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
> What do you think of adding your program to Superseeker?  It sounds 
like
> this would definitely be worth doing.
>
> By the way, can you do anything with A122536?  We have 200 terms, but 
no
> formula or recurrence!
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
> pew at worldwidemann.com> wrote:
>
> > Well, it turns out the first eight elements of A000001 satisfy the, 
umm,
> > "slightly exotic" recurrence relation
> >
> >   a(1) = 1
> >   a(2) = 1
> >   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
> >
> > ;)
> >
> > In earnest, while I doubt that brute forcing formulas will bring any
> > insight into sequences that have baffled mathematicians for 
centuries
> > with their irregularity, what might indeed be interesting is to run 
the
> > system not on one sequence, but on tens of thousands, all of which 
have
> > no closed-form expression associated with them (is there a way to 
query
> > those on OEIS?). In a matter of days, Sequencer would likely return 
a
> > hundred or so closed forms, some of which may prove correct, which 
could
> > then be investigated rigorously.
> >
> > For such a search, I should probably also add a lot more 
combinatorial
> > and number theoretic primitives to the formula generator ? whenever 
I
> > randomly browse around OEIS, most of the sequences seem to be 
counting
> > problems of some kind.
> >
> > Best regards
> > Philipp
> >
> >
> >
> >
> > On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> > > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
> > olivier.gerard at gmail.com>
> > > wrote:
> > >
> > > >
> > > > It would be nice to test it on "hard" sequences and other 
sequences
> > without
> > > > formula.
> > > >
> > > >
> > > >
> > > For example:  http://oeis.org/A000001, the number of groups of 
order n
> > :-)
> > >
> > > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
> > groups
> > > of order n.
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From 2stepan at rambler.ru  Tue Feb 24 21:41:21 2015
From: 2stepan at rambler.ru (=?koi8-r?B?wNLJyiDHxdLB08nNz9c=?=)
Date: Tue, 24 Feb 2015 23:41:21 +0300
Subject: [seqfan] magma calculator
In-Reply-To: <1424810477.253256.19611.44231@mail.rambler.ru>
References: <1424810477.253256.19611.44231@mail.rambler.ru>
Message-ID: <1424810481.1426.15492.48037@mail.rambler.ru>


Dear SeqFans. 

Magma calculator: a(27) = ? and a(64) = ? if  a(n) = smallest k such that k^n + n is prime: 

1, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 417, 2, 1, 0, 1, 0, 81, 

76, 1, 0, 55, 28, 15, (a(27) = ?), 1, 0, 1, 0, 117, 230, 3, 12, 1, 0, 375, 2, 1, 

0, 1, 0, 25, 218, 1, 0, 7, 100, 993, 28, 1, 0, 13, 252, 183, 226, 1, 0, 1, 

0, 777, 1294, (a(64) = ?), 1806, ...

Thanks, JSG

From olivier.gerard at gmail.com  Wed Feb 25 00:26:31 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Wed, 25 Feb 2015 00:26:31 +0100
Subject: [seqfan] Re: magma calculator
In-Reply-To: <1424810481.1426.15492.48037@mail.rambler.ru>
References: <1424810477.253256.19611.44231@mail.rambler.ru>
 <1424810481.1426.15492.48037@mail.rambler.ru>
Message-ID: <CAAcpPSaO6bZFt_T9TU9HtBxUC4mv9O7dPzDA7Ta8sqU7yPNtAw@mail.gmail.com>

Dear Youri,

If you are on seqfan, why don't use the OEIS first to gain more knowledge ?

Look at http://oeis.org/A072883

and you will have the explanation why a(27) and a(64) have no solutions.

A good rule to lookup something in the OEIS is : never assume that your
own conventions about initial terms, offset, meaning of 0 and 1 have been
chosen
by everyone.



Olivier

PS: please next time, find a more appropriate title for your mail. What you
are discussing
is not the magma calculator but a particular computation you did with it.






On Tue, Feb 24, 2015 at 9:41 PM, ???? ????????? <2stepan at rambler.ru> wrote:

>
> Dear SeqFans.
> Magma calculator: a(27) = ? and a(64) = ? if  a(n) = smallest k such that
> k^n + n is prime:
> 1, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 417, 2, 1, 0, 1, 0, 81,
> 76, 1, 0, 55, 28, 15, (a(27) = ?), 1, 0, 1, 0, 117, 230, 3, 12, 1, 0, 375,
> 2, 1,
> 0, 1, 0, 25, 218, 1, 0, 7, 100, 993, 28, 1, 0, 13, 252, 183, 226, 1, 0, 1,
> 0, 777, 1294, (a(64) = ?), 1806, ...
>
> Thanks, JSG
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From israel at math.ubc.ca  Wed Feb 25 00:30:45 2015
From: israel at math.ubc.ca (israel at math.ubc.ca)
Date: 24 Feb 2015 15:30:45 -0800
Subject: [seqfan] Re: magma calculator
In-Reply-To: <1424810481.1426.15492.48037@mail.rambler.ru>
References: <1424810477.253256.19611.44231@mail.rambler.ru>
 <1424810481.1426.15492.48037@mail.rambler.ru>
Message-ID: <Prayer.1.3.5.1502241530450.7384@viol.math.ubc.ca>


x^27 + 27 is divisible by x^9 + 3, x^64 + 64 is divisible by x^32-4*x^16+8.

Cheers,
Robert

On Feb 24 2015, ???? ????????? wrote:

>
>Dear SeqFans. 
>
> Magma calculator: a(27) = ? and a(64) = ? if a(n) = smallest k such that 
> k^n + n is prime:
>
>1, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 417, 2, 1, 0, 1, 0, 81, 
>
> 76, 1, 0, 55, 28, 15, (a(27) = ?), 1, 0, 1, 0, 117, 230, 3, 12, 1, 0, 
> 375, 2, 1,
>
>0, 1, 0, 25, 218, 1, 0, 7, 100, 993, 28, 1, 0, 13, 252, 183, 226, 1, 0, 1, 
>
>0, 777, 1294, (a(64) = ?), 1806, ...
>
>Thanks, JSG
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>


From charles.greathouse at case.edu  Wed Feb 25 07:34:47 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Wed, 25 Feb 2015 01:34:47 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <1424810256.2771.27.camel@worldwidemann.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
 <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
 <1424810256.2771.27.camel@worldwidemann.com>
Message-ID: <CAAkfSGLZzqWEQ5xQiGgBBwh2mQzJXZ9sandhyO4-aovytL=WiQ@mail.gmail.com>

There are about 100,000 sequences with %F lines and about 150,000 without.
It's probably worthwhile to run it on all the sequences in
oeis.org/stripped.gz.

I think adding the Sequencer to the Superseeker would be great -- at least
through depth 5, which takes a second or two, and possibly to depth 6
depending on our free processor time (in my experiments this takes a few
minutes). I imagine the easiest way would be to run it as a black box,
dumping the result to a temp file?

Yangchen Pan and Max Alekseyev were working on a project looking for
relations between OEIS sequences, they may also have useful information.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Tue, Feb 24, 2015 at 3:37 PM, Philipp Emanuel Weidmann <
pew at worldwidemann.com> wrote:

> Sounds good, how would that work? Sequencer already has a public API
> (documented at https://github.com/p-e-w/sequencer#api) so integration
> should be easy as long as Superseeker has a way to interface with a JVM
> library.
>
> As for A122536, nothing so far I'm afraid. I really would like to run a
> mass search on sequences without formulas though. Do you perhaps know of
> a way to find just those on OEIS? Soon the batch of performance
> improvements I'm currently working on will be finished, and then
> Sequencer should be able to search all depth 6 formulas for more than
> 1000 Sequences per day. Also, a batch mode could be implemented, which
> would allow the program to process a large number of sequences at once,
> dramatically improving performance for this use case. Indeed, all of
> OEIS could be checked this way in about a week probably ? which would
> also be interesting for sequences that already *have* formulas, as some
> of them may possess interesting alternative forms, or be incorrect.
>
> Best regards
> Philipp
>
>
>
>
>
> On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
> > What do you think of adding your program to Superseeker?  It sounds like
> > this would definitely be worth doing.
> >
> > By the way, can you do anything with A122536?  We have 200 terms, but no
> > formula or recurrence!
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
> > pew at worldwidemann.com> wrote:
> >
> > > Well, it turns out the first eight elements of A000001 satisfy the,
> umm,
> > > "slightly exotic" recurrence relation
> > >
> > >   a(1) = 1
> > >   a(2) = 1
> > >   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
> > >
> > > ;)
> > >
> > > In earnest, while I doubt that brute forcing formulas will bring any
> > > insight into sequences that have baffled mathematicians for centuries
> > > with their irregularity, what might indeed be interesting is to run the
> > > system not on one sequence, but on tens of thousands, all of which have
> > > no closed-form expression associated with them (is there a way to query
> > > those on OEIS?). In a matter of days, Sequencer would likely return a
> > > hundred or so closed forms, some of which may prove correct, which
> could
> > > then be investigated rigorously.
> > >
> > > For such a search, I should probably also add a lot more combinatorial
> > > and number theoretic primitives to the formula generator ? whenever I
> > > randomly browse around OEIS, most of the sequences seem to be counting
> > > problems of some kind.
> > >
> > > Best regards
> > > Philipp
> > >
> > >
> > >
> > >
> > > On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> > > > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
> > > olivier.gerard at gmail.com>
> > > > wrote:
> > > >
> > > > >
> > > > > It would be nice to test it on "hard" sequences and other sequences
> > > without
> > > > > formula.
> > > > >
> > > > >
> > > > >
> > > > For example:  http://oeis.org/A000001, the number of groups of
> order n
> > > :-)
> > > >
> > > > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
> > > groups
> > > > of order n.
> > > >
> > > > _______________________________________________
> > > >
> > > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From antti.karttunen at gmail.com  Wed Feb 25 09:12:54 2015
From: antti.karttunen at gmail.com (Antti Karttunen)
Date: Wed, 25 Feb 2015 10:12:54 +0200
Subject: [seqfan] Re: Purely algorithmic number sequence identification
Message-ID: <CAB+0_=nG2LrDnSvMZnBCuQY3A53vJacH-PKdkCrjkP2vrc6OUw@mail.gmail.com>

On Tue, Feb 24, 2015 at 3:06 PM,  <seqfan-request at list.seqfan.eu> wrote:

> Message: 12
> Date: Mon, 23 Feb 2015 19:21:07 +0100
> From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
> To: seqfan at list.seqfan.eu
> Subject: [seqfan]  Re: Purely algorithmic number sequence
>         identification
> Message-ID: <1424715667.2631.30.camel at worldwidemann.com>
> Content-Type: text/plain; charset="UTF-8"
>
> Well, it turns out the first eight elements of A000001 satisfy the, umm,
> "slightly exotic" recurrence relation
>
>   a(1) = 1
>   a(2) = 1
>   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>
> ;)
>
> In earnest, while I doubt that brute forcing formulas will bring any
> insight into sequences that have baffled mathematicians for centuries
> with their irregularity, what might indeed be interesting is to run the
> system not on one sequence, but on tens of thousands, all of which have
> no closed-form expression associated with them (is there a way to query
> those on OEIS?). In a matter of days, Sequencer would likely return a
> hundred or so closed forms, some of which may prove correct, which could
> then be investigated rigorously.
>
> For such a search, I should probably also add a lot more combinatorial
> and number theoretic primitives to the formula generator ? whenever I
> randomly browse around OEIS, most of the sequences seem to be counting
> problems of some kind.

Kudos for interesting development!

Yes, especially number theoretic primitives would be welcome, because
for now your system does not exactly shine on any such sequences. For
example, although it correctly identifies factorials:

http://www.sequenceboss.org/?q=1%2C2%2C6%2C24%2C120%2C720%2C5040

then for primorials https://oeis.org/A002110 it remains baffled:
http://www.sequenceboss.org/?q=1%2C+2%2C+6%2C+30%2C+210%2C+2310%2C+30030%2C+510510%2C+9699690

Neither any success with the squares of primes:
http://www.sequenceboss.org/?q=4%2C+9%2C+25%2C+49%2C+121%2C+169%2C+289

(Not to speak about any of A000005, A000010 or A000203).

Now, when testing the third row of "Ludic array"
https://oeis.org/A255127

http://www.sequenceboss.org/?q=5%2C+19%2C+35%2C+49%2C+65%2C+79%2C+95%2C+109%2C+125%2C+139%2C+155%2C+169

the SequenceBoss, guesses a working recurrence for it:

a_1 = 5, a_2 = 19, a3 = 35, a_n = a_{n-2} - a_{n-3} + a_{n-1} for n >= 4

(This mirrors the recurrence a(n) = a(n-1) + a(n-2) - a(n-3), n>=4
given for A007310 by Roger Bagula)


No such success with the later rows of A255127 though:

http://www.sequenceboss.org/?q=7%2C+31%2C+59%2C+85%2C+113%2C+137%2C+163%2C+191%2C+217%2C+241

http://www.sequenceboss.org/?q=11%2C++55%2C+103%2C+151%2C+203%2C+251%2C++299%2C++343%2C++391%2C++443

(although when looking at their graphs, they all look awfully linear...)


Cheers,

Antti

>
> Best regards
> Philipp
>


From antti.karttunen at gmail.com  Wed Feb 25 10:24:23 2015
From: antti.karttunen at gmail.com (Antti Karttunen)
Date: Wed, 25 Feb 2015 11:24:23 +0200
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <CAB+0_=nG2LrDnSvMZnBCuQY3A53vJacH-PKdkCrjkP2vrc6OUw@mail.gmail.com>
References: <CAB+0_=nG2LrDnSvMZnBCuQY3A53vJacH-PKdkCrjkP2vrc6OUw@mail.gmail.com>
Message-ID: <CAB+0_=nbQGvf_PX3HdGK0hB6TkJXL1_tsxurCtydeZ+G1fyCtQ@mail.gmail.com>

Neither any success with A000265
http://www.sequenceboss.org/?q=1%2C+1%2C+3%2C+1%2C+5%2C+3%2C+7%2C+1%2C+9%2C+5%2C+11%2C+3%2C+13%2C+7%2C+15%2C+1%2C+17
(or the associated A003602)

Nor with sequences like:
https://oeis.org/A126760
or:
https://oeis.org/A254104
(nor its inverse A254103).


These kinds of sequences are very common in OEIS, where one doesn't
recurse with some constant offset decremented from n (as in a(n-1) +
a(n-2)) but with n/2 (if n is even) and say, with (n-1)/2 if n is odd.

Maybe also some "p-adic primitives" would be good, e.g. applying A007814 ?


Best,

Antti


On Wed, Feb 25, 2015 at 10:12 AM, Antti Karttunen
<antti.karttunen at gmail.com> wrote:
> On Tue, Feb 24, 2015 at 3:06 PM,  <seqfan-request at list.seqfan.eu> wrote:
>
>> Message: 12
>> Date: Mon, 23 Feb 2015 19:21:07 +0100
>> From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
>> To: seqfan at list.seqfan.eu
>> Subject: [seqfan]  Re: Purely algorithmic number sequence
>>         identification
>> Message-ID: <1424715667.2631.30.camel at worldwidemann.com>
>> Content-Type: text/plain; charset="UTF-8"
>>
>> Well, it turns out the first eight elements of A000001 satisfy the, umm,
>> "slightly exotic" recurrence relation
>>
>>   a(1) = 1
>>   a(2) = 1
>>   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>>
>> ;)
>>
>> In earnest, while I doubt that brute forcing formulas will bring any
>> insight into sequences that have baffled mathematicians for centuries
>> with their irregularity, what might indeed be interesting is to run the
>> system not on one sequence, but on tens of thousands, all of which have
>> no closed-form expression associated with them (is there a way to query
>> those on OEIS?). In a matter of days, Sequencer would likely return a
>> hundred or so closed forms, some of which may prove correct, which could
>> then be investigated rigorously.
>>
>> For such a search, I should probably also add a lot more combinatorial
>> and number theoretic primitives to the formula generator ? whenever I
>> randomly browse around OEIS, most of the sequences seem to be counting
>> problems of some kind.
>
> Kudos for interesting development!
>
> Yes, especially number theoretic primitives would be welcome, because
> for now your system does not exactly shine on any such sequences. For
> example, although it correctly identifies factorials:
>
> http://www.sequenceboss.org/?q=1%2C2%2C6%2C24%2C120%2C720%2C5040
>
> then for primorials https://oeis.org/A002110 it remains baffled:
> http://www.sequenceboss.org/?q=1%2C+2%2C+6%2C+30%2C+210%2C+2310%2C+30030%2C+510510%2C+9699690
>
> Neither any success with the squares of primes:
> http://www.sequenceboss.org/?q=4%2C+9%2C+25%2C+49%2C+121%2C+169%2C+289
>
> (Not to speak about any of A000005, A000010 or A000203).
>
> Now, when testing the third row of "Ludic array"
> https://oeis.org/A255127
>
> http://www.sequenceboss.org/?q=5%2C+19%2C+35%2C+49%2C+65%2C+79%2C+95%2C+109%2C+125%2C+139%2C+155%2C+169
>
> the SequenceBoss, guesses a working recurrence for it:
>
> a_1 = 5, a_2 = 19, a3 = 35, a_n = a_{n-2} - a_{n-3} + a_{n-1} for n >= 4
>
> (This mirrors the recurrence a(n) = a(n-1) + a(n-2) - a(n-3), n>=4
> given for A007310 by Roger Bagula)
>
>
> No such success with the later rows of A255127 though:
>
> http://www.sequenceboss.org/?q=7%2C+31%2C+59%2C+85%2C+113%2C+137%2C+163%2C+191%2C+217%2C+241
>
> http://www.sequenceboss.org/?q=11%2C++55%2C+103%2C+151%2C+203%2C+251%2C++299%2C++343%2C++391%2C++443
>
> (although when looking at their graphs, they all look awfully linear...)
>
>
> Cheers,
>
> Antti
>
>>
>> Best regards
>> Philipp
>>


From apovolot at gmail.com  Wed Feb 25 01:32:49 2015
From: apovolot at gmail.com (apovolot at gmail.com)
Date: Tue, 24 Feb 2015 19:32:49 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <8D21E9F22268966-720-A8A7C@webmail-vm046.sysops.aol.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
 <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
 <1424810256.2771.27.camel@worldwidemann.com>
 <8D21E9F22268966-720-A8A7C@webmail-vm046.sysops.aol.com>
Message-ID: <243EA8F9-2612-43D6-AFAF-2E42A32F53CA@gmail.com>

Could usage of the prefix
formula: 
be somehow employed to the sequences with no formulas present at all ?

> On Feb 24, 2015, at 6:17 PM, Frank Adams-Watters <franktaw at netscape.net> wrote:
> 
> If you search in the native format for sequences without "%F" lines, you will find the sequences with no formulas present at all. This still leaves a larger number of sequences for which some formula has been added, but not a formula specifically to define the sequence.
> 
> Franklin T. Adams-Watters
> 
> -----Original Message-----
> From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
> To: seqfan <seqfan at list.seqfan.eu>
> Sent: Tue, Feb 24, 2015 5:09 pm
> Subject: [seqfan]  Re: Purely algorithmic number sequence identification
> 
> 
> Sounds good, how would that work? Sequencer already has a public API
> (documented at https://github.com/p-e-w/sequencer#api) so integration
> should be easy as long as Superseeker has a way to interface with a JVM
> library.
> 
> As for A122536, nothing so far I'm afraid. I really would like to run a
> mass search on sequences without formulas though. Do you perhaps know of
> a way to find just those on OEIS? Soon the batch of performance
> improvements I'm currently working on will be finished, and then
> Sequencer should be able to search all depth 6 formulas for more than
> 1000 Sequences per day. Also, a batch mode could be implemented, which
> would allow the program to process a large number of sequences at once,
> dramatically improving performance for this use case. Indeed, all of
> OEIS could be checked this way in about a week probably ? which would
> also be interesting for sequences that already *have* formulas, as some
> of them may possess interesting alternative forms, or be incorrect.
> 
> Best regards
> Philipp
> 
> 
> 
> 
> 
>> On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
>> What do you think of adding your program to Superseeker?  It sounds
> like
>> this would definitely be worth doing.
>> 
>> By the way, can you do anything with A122536?  We have 200 terms, but
> no
>> formula or recurrence!
>> 
>> Best regards
>> Neil
>> 
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
> NJ.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>> 
>> 
>> On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
>> pew at worldwidemann.com> wrote:
>> 
>> > Well, it turns out the first eight elements of A000001 satisfy the,
> umm,
>> > "slightly exotic" recurrence relation
>> >
>> >   a(1) = 1
>> >   a(2) = 1
>> >   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>> >
>> > ;)
>> >
>> > In earnest, while I doubt that brute forcing formulas will bring any
>> > insight into sequences that have baffled mathematicians for
> centuries
>> > with their irregularity, what might indeed be interesting is to run
> the
>> > system not on one sequence, but on tens of thousands, all of which
> have
>> > no closed-form expression associated with them (is there a way to
> query
>> > those on OEIS?). In a matter of days, Sequencer would likely return
> a
>> > hundred or so closed forms, some of which may prove correct, which
> could
>> > then be investigated rigorously.
>> >
>> > For such a search, I should probably also add a lot more
> combinatorial
>> > and number theoretic primitives to the formula generator ? whenever
> I
>> > randomly browse around OEIS, most of the sequences seem to be
> counting
>> > problems of some kind.
>> >
>> > Best regards
>> > Philipp
>> >
>> >
>> >
>> >
>> > On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
>> > > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
>> > olivier.gerard at gmail.com>
>> > > wrote:
>> > >
>> > > >
>> > > > It would be nice to test it on "hard" sequences and other
> sequences
>> > without
>> > > > formula.
>> > > >
>> > > >
>> > > >
>> > > For example:  http://oeis.org/A000001, the number of groups of
> order n
>> > :-)
>> > >
>> > > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
>> > groups
>> > > of order n.
>> > >
>> > > _______________________________________________
>> > >
>> > > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>> >
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>> 
>> _______________________________________________
>> 
>> Seqfan Mailing list - http://list.seqfan.eu/
> 
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/
> 
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/


From rselcoe at entouchonline.net  Wed Feb 25 06:35:48 2015
From: rselcoe at entouchonline.net (Bob Selcoe)
Date: Tue, 24 Feb 2015 23:35:48 -0600
Subject: [seqfan] Re: Improved lower bound for A250000
In-Reply-To: <CAEG8PYvDamRCbDj9dfC=cyeLrpYLThJGPZyCqr6QMvvt_wEKUQ@mail.gmail.com>
References: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
 <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>
 <CAEG8PYvDamRCbDj9dfC=cyeLrpYLThJGPZyCqr6QMvvt_wEKUQ@mail.gmail.com>
Message-ID: <0D1F3B422EDF45F3B72AA633DCB86882@OwnerPC>

Hi Benoit,

Excellent!  This certainly is an improvement.

But I'm having a little difficulty following how you've obtained the upper 
and lower bounds, as well as your description of coordinates.

So for my n=24 a(n)=83 board, wouldn't you also say the queens of one color 
are in the two regions x<1/4, y<1/2, x<y<x+1/3
and 1/2<x<3/4, y<x-1/3, y<1-x, while the queens of the other color are 
obtained by central symmetry (or at least something approximating central 
symmetry)???

So I don't see how the definitions between your and my configurations 
differ; that is, when you say:

>> I obtained these coefficients by equalizing the lengths of the "opposite" 
>> boundaries of the armies  (this already improves (by 1) on the "Board 4" 
>> example of the webpage).

I'm not sure what you "equalized" to gain the improvement.

But still, there is definite improvement.

I probably won't have time to look into a structural pattern for n = 4m for 
several days; my guess is one exists based on your approach, which will 
improve upon mine.  Will you have a chance to see if such a pattern exists?

Best Wishes,
Bob Selcoe

--------------------------------------------------
From: "Beno?t Jubin" <benoit.jubin at gmail.com>
Sent: Tuesday, February 24, 2015 11:25 AM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Improved lower bound for A250000

> Dear Rob,
> I improved by one the final board on the webpage by using the same idea as
> for my asymptotic bound, but you are right that in this specific case, the
> result is not centrally symmetric. From the last example on the webpage, I
> made marginal changes along the diagonals (in the [0,1]^2 coordinates)
> y=x+1/3 (deleted 3 Ws, added 5 Bs) and y=x-1/3 (deleted 4 Bs, added 4Ws):
>
> ------------------------
>
> ......WWWWWW............
>
> ......WWWWWW...........W
>
> ......WWWWWW..........WW
>
> ......WWWWWW.........WWW
>
> ......WWWWWW........WWWW
>
> ......WWWWW........WWWWW
>
> .......WWW........WWWWWW
>
> ........W.........WWWWWW
>
> ..................WWWWWW
>
> ..................WWWWW.
>
> ..................WWWW..
>
> ..................WWW...
>
> ....BB..................
>
> ...BBB..................
>
> ..BBBB..................
>
> .BBBBB..................
>
> BBBBBB..........B.......
>
> BBBBBB.........BBB......
>
> BBBBBB........BBBB......
>
> BBBBB........BBBBB......
>
> BBBB........BBBBBB......
>
> BBB.........BBBBBB......
>
> BB..........BBBBBB......
>
> B...........BBBBBB......
>
> ------------------------
>
>
>
> On Tue, Feb 24, 2015 at 6:13 PM, Rob Pratt <Rob.Pratt at sas.com> wrote:
>
>> Please share your n =24 solution.  Under the central symmetry constraint,
>> I get a maximum of 80, not 84.
>>
>> -----Original Message-----
>> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Beno?t
>> Jubin
>> Sent: Tuesday, February 24, 2015 11:50 AM
>> To: Sequence Fanatics Discussion list
>> Subject: [seqfan] Improved lower bound for A250000
>>
>> Dear seqfans,
>>
>> Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on
>> an (n,n) chessboard.
>>
>> By modifying the Pratt--Selcoe configuration, I improved the best known
>> lower bound from
>> a(n) > (9/4)*(n/4)^2
>> to
>> a(n) > (7/3)*(n/4)^2.
>> I have been sloppy with side effects, but to be on the safe side, let's 
>> say
>> a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the
>> coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the
>> following description.
>>
>> The configuration in the limit n = infinity is as follows: denoting by 
>> x,y
>> in [0,1] the coordinates on the chessboard, the queens of one color are 
>> in
>> the two regions x<1/4, y<1/2, x<y<x+1/3 and 1/2<x<3/4, y<x-1/3, y<1-x and
>> the queens of the other color are obtained by central symmetry. As you 
>> can
>> guess, I obtained these coefficients by equalizing the lengths of the
>> "opposite" boundaries of the armies (this already improves (by 1) on the
>> "Board 4" example of the webpage).
>>
>> Using an easy upper bound, one has asymptotically
>> (2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
>> Anyone to help fill the gap?
>>
>> Best,
>> Benoit
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
> 


From benoit.jubin at gmail.com  Wed Feb 25 23:10:14 2015
From: benoit.jubin at gmail.com (=?UTF-8?Q?Beno=C3=AEt_Jubin?=)
Date: Wed, 25 Feb 2015 23:10:14 +0100
Subject: [seqfan] Re: Improved lower bound for A250000
In-Reply-To: <0D1F3B422EDF45F3B72AA633DCB86882@OwnerPC>
References: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
 <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>
 <CAEG8PYvDamRCbDj9dfC=cyeLrpYLThJGPZyCqr6QMvvt_wEKUQ@mail.gmail.com>
 <0D1F3B422EDF45F3B72AA633DCB86882@OwnerPC>
Message-ID: <CAEG8PYvpUtYRZsQ+FL6OyixBRXXuJpWFd24fcWfF=nG6r0w9HQ@mail.gmail.com>

Dear Rob,

I think that you interpret the coordinates correctly. My configuration is
only a slight modification of yours, but not exactly the same, as you can
see in my example for n=24 (in a previous email of this conversation).
Also, the bound you give on the webpage, namely (after simplification),
a(4m) >= floor( (9/4)*m^2 + m/2 - 3/4 )
made me think that your configuration is given as follows (for n=4m):
One decomposes the chessboard into 16 smaller (m,m) chessboards as follows:
.A.B
.C.D
W.X.
Y.Z.
where the dots are empty chessboards and
A, B, C, D contain the queens of one color
and
W, X, Y, Z contain the queens of the other color.
Borrowing to the language of matrices, the occupied squares are as follows:
A: all squares,
B: strict lower-right half,
C: strict upper quarter, that is, intersection of the strict upper-left
half and the strict upper-right half,
D: upper-left half plus the first subdiagonal,
W: lower-right half,
X: intersection of the strict lower-right half minus the first subdiagonal
and the lower-left half,
Y: upper-left half,
Z: all squares minus the upper-left one.

What I meant by "equalizing the opposite boundaries" is this: in the picture

....|....|......../

....|....|......./.

....|....|....../..

....|.../....../...

....|../....../....

.....\/.......|....

..............|....

..............|.../

..............|../.

..--+.........+--..

./..|..............

/...|..............

....|..............

....|......./\.....

..../....../..|....

.../....../...|....

../......|....|....
./.......|....|....

/........|....|....

each of the lines x=1/4, x=1/2, x=3/4, y=1/2, y=x, y=x+1/3, y=x-1/3,y=1-x
borders a white region and a black region, and the length during which it
borders each is equal. This is how I optimized your solution: by
translating these lines, one adds to the army of one color while removing
from the other color (compensate this on the other pair of regions, to
still have equally sized armies), so one deduces that for the optimal
configuration of this sort, "opposite boundaries" must have same length.


I am mainly interested in asymptotics, where it does not matter whether n
is divisible by 4 or not. But for a given n, not necessarily divisible by
4, I would first draw these regions, and for any given square, if more than
half of it is within the region, I would put a queen. For the 50%-squares,
put queens for one out of the two regions. Finally (possibly not needed),
give or take a few queens on the boundaries to get an admissible
configuration.


Best,

Beno?t





On Wed, Feb 25, 2015 at 6:35 AM, Bob Selcoe <rselcoe at entouchonline.net>
wrote:

> Hi Benoit,
>
> Excellent!  This certainly is an improvement.
>
> But I'm having a little difficulty following how you've obtained the upper
> and lower bounds, as well as your description of coordinates.
>
> So for my n=24 a(n)=83 board, wouldn't you also say the queens of one
> color are in the two regions x<1/4, y<1/2, x<y<x+1/3
> and 1/2<x<3/4, y<x-1/3, y<1-x, while the queens of the other color are
> obtained by central symmetry (or at least something approximating central
> symmetry)???
>
> So I don't see how the definitions between your and my configurations
> differ; that is, when you say:
>
>  I obtained these coefficients by equalizing the lengths of the "opposite"
>>> boundaries of the armies  (this already improves (by 1) on the "Board 4"
>>> example of the webpage).
>>>
>>
> I'm not sure what you "equalized" to gain the improvement.
>
> But still, there is definite improvement.
>
> I probably won't have time to look into a structural pattern for n = 4m
> for several days; my guess is one exists based on your approach, which will
> improve upon mine.  Will you have a chance to see if such a pattern exists?
>
> Best Wishes,
> Bob Selcoe
>
> --------------------------------------------------
> From: "Beno?t Jubin" <benoit.jubin at gmail.com>
> Sent: Tuesday, February 24, 2015 11:25 AM
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Improved lower bound for A250000
>
>
>  Dear Rob,
>> I improved by one the final board on the webpage by using the same idea as
>> for my asymptotic bound, but you are right that in this specific case, the
>> result is not centrally symmetric. From the last example on the webpage, I
>> made marginal changes along the diagonals (in the [0,1]^2 coordinates)
>> y=x+1/3 (deleted 3 Ws, added 5 Bs) and y=x-1/3 (deleted 4 Bs, added 4Ws):
>>
>> ------------------------
>>
>> ......WWWWWW............
>>
>> ......WWWWWW...........W
>>
>> ......WWWWWW..........WW
>>
>> ......WWWWWW.........WWW
>>
>> ......WWWWWW........WWWW
>>
>> ......WWWWW........WWWWW
>>
>> .......WWW........WWWWWW
>>
>> ........W.........WWWWWW
>>
>> ..................WWWWWW
>>
>> ..................WWWWW.
>>
>> ..................WWWW..
>>
>> ..................WWW...
>>
>> ....BB..................
>>
>> ...BBB..................
>>
>> ..BBBB..................
>>
>> .BBBBB..................
>>
>> BBBBBB..........B.......
>>
>> BBBBBB.........BBB......
>>
>> BBBBBB........BBBB......
>>
>> BBBBB........BBBBB......
>>
>> BBBB........BBBBBB......
>>
>> BBB.........BBBBBB......
>>
>> BB..........BBBBBB......
>>
>> B...........BBBBBB......
>>
>> ------------------------
>>
>>
>>
>> On Tue, Feb 24, 2015 at 6:13 PM, Rob Pratt <Rob.Pratt at sas.com> wrote:
>>
>>  Please share your n =24 solution.  Under the central symmetry constraint,
>>> I get a maximum of 80, not 84.
>>>
>>> -----Original Message-----
>>> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Beno?t
>>> Jubin
>>> Sent: Tuesday, February 24, 2015 11:50 AM
>>> To: Sequence Fanatics Discussion list
>>> Subject: [seqfan] Improved lower bound for A250000
>>>
>>> Dear seqfans,
>>>
>>> Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on
>>> an (n,n) chessboard.
>>>
>>> By modifying the Pratt--Selcoe configuration, I improved the best known
>>> lower bound from
>>> a(n) > (9/4)*(n/4)^2
>>> to
>>> a(n) > (7/3)*(n/4)^2.
>>> I have been sloppy with side effects, but to be on the safe side, let's
>>> say
>>> a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the
>>> coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the
>>> following description.
>>>
>>> The configuration in the limit n = infinity is as follows: denoting by
>>> x,y
>>> in [0,1] the coordinates on the chessboard, the queens of one color are
>>> in
>>> the two regions x<1/4, y<1/2, x<y<x+1/3 and 1/2<x<3/4, y<x-1/3, y<1-x and
>>> the queens of the other color are obtained by central symmetry. As you
>>> can
>>> guess, I obtained these coefficients by equalizing the lengths of the
>>> "opposite" boundaries of the armies (this already improves (by 1) on the
>>> "Board 4" example of the webpage).
>>>
>>> Using an easy upper bound, one has asymptotically
>>> (2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
>>> Anyone to help fill the gap?
>>>
>>> Best,
>>> Benoit
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From gladhobo at teksavvy.com  Thu Feb 26 21:34:15 2015
From: gladhobo at teksavvy.com (Hans Havermann)
Date: Thu, 26 Feb 2015 15:34:15 -0500
Subject: [seqfan] A126263
Message-ID: <B1D27FE9-3B6B-4CA9-B2FD-D26DB357F715@teksavvy.com>

I noticed that William Stein's b-file for http://oeis.org/A126263 incorporates an incorrect a(17) that dates to the original sequence submission. One might as well add a(28) which is 73.

From peter.luschny at gmail.com  Thu Feb 26 22:27:34 2015
From: peter.luschny at gmail.com (Peter Luschny)
Date: Thu, 26 Feb 2015 22:27:34 +0100
Subject: [seqfan] Are all sufficiently large highly abundant numbers
	practical?
Message-ID: <CAMMbGZYHW0Rza6=yynvkF68JJHtUu7qRfe7WyHS4d=d1kOze3Q@mail.gmail.com>

Conjecture: (a) Every highly abundant number >10 is practical (A005153).
(b) For every integer k there exists A such that k divides a(n)
for all n>A. Daniel Fischer proved that every highly abundant
number greater than 3, 20, 630 is divisible by 2, 6, 12 respectively.
The first conjecture has been verified for the first 10000 terms.

- Jaycob Coleman, Oct 16 2013
https://oeis.org/A002093

Alaoglu and Erd?s observed that 210 is the largest highly
abundant number to include only one factor of two in its
 prime factorization. All larger highly abundant numbers
 are divisible by four, and by the argument above they
 are all practical. The remaining cases are small enough
 to test individually, and they are all practical. So
 Jaycob Coleman's conjecture is true.

- David Eppstein, 2015-02-26
http://11011110.livejournal.com/305481.html


From rkg at ucalgary.ca  Thu Feb 26 21:40:50 2015
From: rkg at ucalgary.ca (rkg)
Date: Thu, 26 Feb 2015 13:40:50 -0700 (MST)
Subject: [seqfan] A000292 (fwd)
Message-ID: <alpine.LFD.2.11.1502261339450.2122@csl.cs.ucalgary.ca>

Further apologies if you've received multiple copies of this.  R.

---------- Forwarded message ----------
Date: Thu, 26 Feb 2015 13:12:39 -0700 (MST)
From: rkg <rkg at ucalgary.ca>
To: Sequence Fans <seqfan at ext.jussieu.fr>
Subject: A000292 (fwd)

Sorry, my email has been ``upgraded'' and now my address file seems
to be all aglee.  R.

---------- Forwarded message ----------
Date: Thu, 26 Feb 2015 13:03:43 -0700 (MST)
From: rkg <rkg at ucalgary.ca>
To: Neil Sloane <njasloane at gmail.com>,
      Sloane's Dream Team <Antti.Karttunen at gmail.com>, bowerc at usa.net,
      david at research.att.com, David Wilson <davidwwilson at comcast.net>,
      deutsch at duke.poly.edu, djr at nk.ca, dwasserm at earthlink.net,
      editors at seqfan.net, j.mccranie at comcast.net, layman at math.vt.edu,
      mathar at strw.leidenuniv.nl, maxal at cs.ucsd.edu, maxale at gmail.com,
      maximilian.hasler at gmail.com, mlb at well.com, njas at research.att.com,
      noe at sspectra.com, rayjchandler at sbcglobal.net, rgwv at rgwv.com,
      rsc at swtch.com,
      simon.plouffe at gmail.com, simon.plouffe at sympatico.ca,
      somos at grail.cba.csuohio.edu, stefan.steinerberger at gmail.com,
      wasserma at spawar.navy.mil
Subject: A000292

Dear all,
          As my Mother used to say, I'm not a good looker, so
I may have missed someething in A000292.  These are not only
the triangular pyramidal numbers, but also the kind of square
pyramidal numbers you get by using cubes, and insisting that
square faces must always coincide:

1^2, 2^2, 1^2+3^2, 2^2+4^2, 1^2+3^2+5^2, 2^2+4^2+6^2, ...

           R.
1   1  1   1  1  1   1  1  1  1   1  1  1  1  1
      1  1   1  2  1   1  2  2  1   1  2  2  2  1
             1  1  1   1  2  2  1   1  2  3  2  1
                       1  1  1  1   1  2  2  2  1
                                    1  1  1  1  1



From lars.blomberg at visit.se  Fri Feb 27 07:48:50 2015
From: lars.blomberg at visit.se (Lars Blomberg)
Date: Fri, 27 Feb 2015 07:48:50 +0100
Subject: [seqfan] A254042, A254447-A254502
Message-ID: <011301d05259$7224b680$566e2380$@visit.se>



Hello!

 

The sequences A254042, A254447-A254502 are using digits 1-7 respectively.

The corresponding sequences for digits 8 and 9 seem to be missing.

Does anyone know of a reason why this is so?

If not, is it ok to add them?

 

/Lars B

 



From njasloane at gmail.com  Fri Feb 27 20:18:38 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Fri, 27 Feb 2015 14:18:38 -0500
Subject: [seqfan] Re: A254042, A254447-A254502
In-Reply-To: <011301d05259$7224b680$566e2380$@visit.se>
References: <011301d05259$7224b680$566e2380$@visit.se>
Message-ID: <CAAOnSgSuJNSQJvi=uYuXhuiHsKj+Ej4CBj8cu=Lwxy3JcujEXg@mail.gmail.com>

> If not, is it ok to add them?

Certainly!  Please do so!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 27, 2015 at 1:48 AM, Lars Blomberg <lars.blomberg at visit.se>
wrote:

>
>
> Hello!
>
>
>
> The sequences A254042, A254447-A254502 are using digits 1-7 respectively.
>
> The corresponding sequences for digits 8 and 9 seem to be missing.
>
> Does anyone know of a reason why this is so?
>
> If not, is it ok to add them?
>
>
>
> /Lars B
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From peter.luschny at gmail.com  Fri Feb 27 20:47:51 2015
From: peter.luschny at gmail.com (Peter Luschny)
Date: Fri, 27 Feb 2015 20:47:51 +0100
Subject: [seqfan] Re: Are all sufficiently large highly abundant numbers
	practical?
Message-ID: <CAMMbGZbi3shQZY4v2RhE7rzGwodGVMDtjLM81CvFH+L9rPo06Q@mail.gmail.com>

The argument has been updated. Is it convincing now?

Is it appropriate for a nomination for the Riordan Prize?

Peter


From seqfan at jaycobcoleman.33mail.com  Sat Feb 28 04:37:20 2015
From: seqfan at jaycobcoleman.33mail.com (seqfan at jaycobcoleman.33mail.com)
Date: Fri, 27 Feb 2015 19:37:20 -0800 (PST)
Subject: [seqfan] Re: Are all sufficiently large highly abundant numbers
 practical?
Message-ID: <1206331671.6876.1425094640060.JavaMail.root@crow>

Hi Peter,

Coincidentally I just joined the mailing list. I will take some time to try
to understand your argument.

Sincerely,
Jaycob Coleman

On Fri, Feb 27, 2015 at 10:47 AM, Peter Luschny 'peter.luschny at gmail.com'
via 33Mail <sender at mailer.33mail.com> wrote:

> This email was sent to the alias 'seqfan at jaycobcoleman.33mail.com' by '
> seqfan at list.seqfan.eu', and 33Mail forwarded it to you. To block all
> further emails to this alias follow this link :
> http://www.33mail.com/alias/unsub/15f7de3a21d314f8a067d051ce9beea7
> Refer 2 friends to 33Mail and get a Free Premium Upgrade. Go to this url
> to get your referral link http://www.33mail.com/dashboard.
>
> The argument has been updated. Is it convincing now?
>
> Is it appropriate for a nomination for the Riordan Prize?
>
> Peter
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Supercollider? I 'ardly know 'er!


From olivier.gerard at gmail.com  Sat Feb 28 07:02:03 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Sat, 28 Feb 2015 07:02:03 +0100
Subject: [seqfan] Welcome to seqfan (was Re: Are all sufficiently large
 highly abundant numbers practical?)
Message-ID: <CAAcpPSYumjws6HCypYozGWUyewBEbXc2KcKiWBapvNg5Pgqu5g@mail.gmail.com>

On Sat, Feb 28, 2015 at 4:37 AM, <seqfan at jaycobcoleman.33mail.com> wrote:

> Hi Peter,
>
> Coincidentally I just joined the mailing list.


Dear Jaycob,

Welcome to seqfan.


> I will take some time to try
> to understand your argument.
>
> Sincerely,
> Jaycob Coleman
>
>
There are several hundreds of subscribers to seqfan.
The following advice applies to them as well:

For your future posts, please take some time to

 - ponder that your message will be archived and publicly accessible

 - consider if your message is better sent privately to a few recipients
instead of the list

 - consider if you are enhancing the signal-to-noise ratio

 - cut out non relevant parts of previous posts (everyone has received them)

 - change the subject line if you have ... changed the subject

 - check you have configured your computer and selected your email address
and provider
to avoid end signatures,  mail server messages, advertising insertions,
legal disclaimers

 - remember that the moderator cannot edit your message for you. He can only
   forward it, reject it or ask you to re-post a better version.

 - communicate directly with the administrator through
seqfan-owner at list.seqfan.eu
if you have a question about the list, your subscription, proper
netiquette, etc.

With my best regards,

Olivier G?rard
Seqfan Mailing List Administrator


> On Fri, Feb 27, 2015 at 10:47 AM, Peter Luschny 'peter.luschny at gmail.com'
> via 33Mail <sender at mailer.33mail.com> wrote:
>
> > This email was sent to the alias 'seqfan at jaycobcoleman.33mail.com' by '
> > seqfan at list.seqfan.eu', and 33Mail forwarded it to you. To block all
> > further emails to this alias follow this link :
> > http://www.33mail.com/alias/unsub/15f7de3a21d314f8a067d051ce9beea7
> > Refer 2 friends to 33Mail and get a Free Premium Upgrade. Go to this url
> > to get your referral link http://www.33mail.com/dashboard.
> >
>


From hpd at hpdale.org  Sat Feb 28 14:45:22 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 28 Feb 2015 13:45:22 +0000
Subject: [seqfan] A102515
Message-ID: <CY1PR0401MB1068A724857277A79E884343C6120@CY1PR0401MB1068.namprd04.prod.outlook.com>

	I cannot generate the terms of the above sequence from its definition.
	Best,
	Harvey


From olivier.gerard at gmail.com  Sat Feb 28 14:53:18 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Sat, 28 Feb 2015 14:53:18 +0100
Subject: [seqfan] Re: A102515
In-Reply-To: <CY1PR0401MB1068A724857277A79E884343C6120@CY1PR0401MB1068.namprd04.prod.outlook.com>
References: <CY1PR0401MB1068A724857277A79E884343C6120@CY1PR0401MB1068.namprd04.prod.outlook.com>
Message-ID: <CAAcpPSYbLk+UZK83k7mH4CXxkRYbiOtM6CoZLCC8u20kvO7TFw@mail.gmail.com>

I agree.

It seems to match

Table[1 + Floor[Sqrt[2 n - 1]], {n, 1, 83}]

instead of

Table[ Floor[Sqrt[2 n + 1]], {n, 1, 83}]


On Sat, Feb 28, 2015 at 2:45 PM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         I cannot generate the terms of the above sequence from its
> definition.
>         Best,
>         Harvey
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Sat Feb 28 17:25:39 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Sat, 28 Feb 2015 11:25:39 -0500
Subject: [seqfan] Re: A102515
In-Reply-To: <CAAcpPSYbLk+UZK83k7mH4CXxkRYbiOtM6CoZLCC8u20kvO7TFw@mail.gmail.com>
References: <CY1PR0401MB1068A724857277A79E884343C6120@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CAAcpPSYbLk+UZK83k7mH4CXxkRYbiOtM6CoZLCC8u20kvO7TFw@mail.gmail.com>
Message-ID: <CAAOnSgT2tM0zEaF4K7YumKtiL-0rbqs5YxdqhPgjhkc9UaVOAw@mail.gmail.com>

please edit it accordingly!  In fact perhaps you should
replace it with two sequences (old values + new defn,
old defn + new values)!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Feb 28, 2015 at 8:53 AM, Olivier Gerard <olivier.gerard at gmail.com>
wrote:

> I agree.
>
> It seems to match
>
> Table[1 + Floor[Sqrt[2 n - 1]], {n, 1, 83}]
>
> instead of
>
> Table[ Floor[Sqrt[2 n + 1]], {n, 1, 83}]
>
>
> On Sat, Feb 28, 2015 at 2:45 PM, Harvey P. Dale <hpd at hpdale.org> wrote:
>
> >         I cannot generate the terms of the above sequence from its
> > definition.
> >         Best,
> >         Harvey
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Sat Feb 28 18:40:22 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Sat, 28 Feb 2015 12:40:22 -0500
Subject: [seqfan] Bob Selcoe's version of the EKG and Yellowstone
 permutations A064413 and A098550
Message-ID: <CAAOnSgQcRCxm7tj24abB9B3=gsVWae4P6iuNbe9_podV1-L69Q@mail.gmail.com>

Dear Sequence Fans, Bob Selcoe recently submitted a lovely new sequence,
A255582.
Like A064413 (the EKG sequence) and A098550 (the Yellowstone Permutation,
subject of our recent arXiv:1501.01669) it is a permutation of the natural
numbers.
The definition is closer to that of A098550, but the graph is more like
that of A064413.  It would be nice to have a better understanding of
what is going on here!

Some associated sequences are A255479, A255480, A255481, A255482,
all of which need b-files, and A064664 (the inverse perm to the EKG
sequence A064413)  could
use at least a 10,000-term b-file.

Vladimir Shevelev's A254077 is of the same ilk, but here there is
no proof yet that it is a permutation of the positive integers: such a
proof is badly needed.
The cross-references in A098550 list many other related sequences that need
work.

This is all strawberry ice-cream for anyone who likes sequences.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


From 2stepan at rambler.ru  Mon Feb 23 08:59:16 2015
From: 2stepan at rambler.ru (=?koi8-r?B?wNLJyiDHxdLB08nNz9c=?=)
Date: Mon, 23 Feb 2015 07:59:16 -0000
Subject: [seqfan] 7...
In-Reply-To: <1424678353.15294.15613.59949@mail.rambler.ru>
References: <1424678353.15294.15613.59949@mail.rambler.ru>
Message-ID: <1424678355.225932.3140.63498@mail.rambler.ru>





Dear SeqFans. 

Primes p such that 15p -/+ 2, 15p -/+ 4 and 15p -/+ 8 are all primes: 7, ... What in the next ( >10^9 ) one? 

P.S. 

Numbers n such that 15n -/+ 2, 15n -/+ 4 and 15n -/+ 8 are all primes: 7, 1071, 1295, 2919, 72751, ... (not in OEIS). 

Primes p such that (15p - 4, 15p - 2, 15p + 2, 15p + 4) is a prime quadruplet: 7, 13, 139, 1049, 4481, ... (not in OEIS). 

Thanks, JSG

.

From arndt at jjj.de  Sun Feb  1 10:22:45 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Sun, 1 Feb 2015 10:22:45 +0100
Subject: [seqfan] polyominoes on square lattice by symmetry
Message-ID: <20150201092245.GA5191@jjj.de>

About
  P. Leroux, E. Rassart, A. Robitaille,
  <a href="http://dx.doi.org/10.1006/aama.1998.0601">
  Enumeration of Symmetry Classes of Convex Polyominoes in the Square Lattice</a>
  Advances in Applied Mathematics, vol.21, no.3, pp.343-380, (October-1998).

Could someone check which sequences given on
p.377 are missing in the OEIS?

At least 1,1,2,7,17,50,131,363,924,2380 is missing.

When entering the seqs please spell out the symmetry type
(I cannot do this, that's why am asking on the list).

Best,  jj



From info at polprimos.com  Sun Feb  1 02:11:01 2015
From: info at polprimos.com (Omar E. Pol)
Date: Sat, 31 Jan 2015 22:11:01 -0300
Subject: [seqfan] A253072.
Message-ID: <20150201011101.M80143@polprimos.com>

Dear Neil,

An observation.
In the sequences A050476 and A253072 we have that: 

a(0) = 1
a(1) = 7
a(3) = 95
a(7) = 18447

A253072(2^k-1) = A050476(2^k-1), 0<=k<=m, where m is at least 3. 

Best regards. 

Omar E. Pol


From arndt at jjj.de  Sun Feb  1 11:00:15 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Sun, 1 Feb 2015 11:00:15 +0100
Subject: [seqfan] honeycomb polyominoes
Message-ID: <20150201100015.GA5352@jjj.de>

Similar to the message before:

Dominique Gouyou-Beauchamps, Pierre Leroux,
<a href="http://dx.doi.org/10.1016/j.tcs.2005.08.025">
Enumeration of Symmetry Classes of Convex Polyominoes on the Honeycomb Lattice</a>,
Theoretical Computer Science, vol.346, no.2-3, pp.307-334, (November-2005).

p.320:
1
3
11
38
120
348
939
2412
5973
14394
34056
79602
184588
426036
980961
2256420
5189577
11939804
27485271
63308532
145903992
336418179
775996665
1790486717
4132195707
9538127076
22018993552
50835685427
117372288297
271006745255
625758286777
1444911247194
3336422923431
7704147029616
17789770663899
41078790416848
94856243572216
219035659925172
505782887350567
1167921607616731
2696891148564180
6227492958077133
14380140755028117
33205732845460311
76676631829002129
177056959135248647
408849042325490952
944089080678393018
2180032500563641911
5033997137232724122
11624197004721262104
26841881829357335687


And, at end of page:
0, 0, 1, 0, 3, 2, 12, 18, 59, 120, 318, 714, 1743, ...


Also p.322: 1, 1, 3, 6, 15, 38, 91, 222, 528, 1250, ...

Also several seqs on p.333


Best,  jj


From njasloane at gmail.com  Sun Feb  1 19:35:37 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Sun, 1 Feb 2015 13:35:37 -0500
Subject: [seqfan] Re: A253072.
In-Reply-To: <20150201011101.M80143@polprimos.com>
References: <20150201011101.M80143@polprimos.com>
Message-ID: <CAAOnSgTtnjbzYHGjrP+jWg2ZgirDjX8BObdKcFFu_fNRBMhAdA@mail.gmail.com>

Interesting comment!  Of course it might be a coincidence.  Still, I added
it to A253072.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Jan 31, 2015 at 8:11 PM, Omar E. Pol <info at polprimos.com> wrote:

> Dear Neil,
>
> An observation.
> In the sequences A050476 and A253072 we have that:
>
> a(0) = 1
> a(1) = 7
> a(3) = 95
> a(7) = 18447
>
> A253072(2^k-1) = A050476(2^k-1), 0<=k<=m, where m is at least 3.
>
> Best regards.
>
> Omar E. Pol
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From arndt at jjj.de  Mon Feb  2 19:18:21 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Mon, 2 Feb 2015 19:18:21 +0100
Subject: [seqfan] Re: polyominoes on square lattice by symmetry
In-Reply-To: <20150201092245.GA5191@jjj.de>
References: <20150201092245.GA5191@jjj.de>
Message-ID: <20150202181821.GA6579@jjj.de>

Will do all of this (incl. other message) myself,
but may well be in several weeks from now.

Best regards,  jj

* Joerg Arndt <arndt at jjj.de> [Feb 01. 2015 12:03]:
> About
>   P. Leroux, E. Rassart, A. Robitaille,
>   <a href="http://dx.doi.org/10.1006/aama.1998.0601">
>   Enumeration of Symmetry Classes of Convex Polyominoes in the Square Lattice</a>
>   Advances in Applied Mathematics, vol.21, no.3, pp.343-380, (October-1998).
> 
> Could someone check which sequences given on
> p.377 are missing in the OEIS?
> 
> At least 1,1,2,7,17,50,131,363,924,2380 is missing.
> 
> When entering the seqs please spell out the symmetry type
> (I cannot do this, that's why am asking on the list).
> 
> Best,  jj
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/


From penson at lptl.jussieu.fr  Tue Feb  3 00:24:08 2015
From: penson at lptl.jussieu.fr (Karol)
Date: Tue, 03 Feb 2015 00:24:08 +0100
Subject: [seqfan] Question on A005572 from K. A. Penson
Message-ID: <54D00718.50007@lptl.jussieu.fr>

Does anybody know how to obtain the close form of A005572(n) ?

Thanking in advance,

     Karol A. Penson


From maxale at gmail.com  Tue Feb  3 00:52:29 2015
From: maxale at gmail.com (Max Alekseyev)
Date: Mon, 2 Feb 2015 18:52:29 -0500
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
In-Reply-To: <54D00718.50007@lptl.jussieu.fr>
References: <54D00718.50007@lptl.jussieu.fr>
Message-ID: <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>

Hi Karol,

There is a formula

A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,

which expands (with substitution k -> n-2k) into:

A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
(k+1) * 4^(n-2k)

PARI/GP code:

{ A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
* 4^(n-2*k) ) }

Regards,
Max



On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
> Does anybody know how to obtain the close form of A005572(n) ?
>
> Thanking in advance,
>
>     Karol A. Penson
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/


From israel at math.ubc.ca  Tue Feb  3 02:46:31 2015
From: israel at math.ubc.ca (israel at math.ubc.ca)
Date: 02 Feb 2015 17:46:31 -0800
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
In-Reply-To: <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>
References: <54D00718.50007@lptl.jussieu.fr>
 <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>
Message-ID: <Prayer.1.3.5.1502021746310.15725@viol.math.ubc.ca>

And, according to Maple, these sums can be written as a hypergeometric 
function:

A005572(n) = 4^n*hypergeom([-n/2, (1-n)/2], [2], 1/4)

Cheers,
Robert

On Feb 2 2015, Max Alekseyev wrote:

>Hi Karol,
>
>There is a formula
>
>A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,
>
>which expands (with substitution k -> n-2k) into:
>
>A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
>(k+1) * 4^(n-2k)
>
>PARI/GP code:
>
>{ A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
>* 4^(n-2*k) ) }
>
>Regards,
>Max
>
>
>
>On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
>> Does anybody know how to obtain the close form of A005572(n) ?
>>
>> Thanking in advance,
>>
>>     Karol A. Penson
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>


From pauldhanna at juno.com  Tue Feb  3 03:15:29 2015
From: pauldhanna at juno.com (Paul D Hanna)
Date: Tue, 3 Feb 2015 02:15:29 GMT
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
Message-ID: <20150202.211529.23111.0@webmail03.dca.untd.com>

Also, 
a(n) = Sum_{k=0..n} binomial(n,k) * 2^(n-k) * binomial(2*k+2, k)/(k+1). 
 
a(n) = Sum_{k=0..n} binomial(n,k) * 2^(n-k) * A000108(k+1). 
 
This can be derived from the relation 
a(n) = [x^n] (1+4*x+x^2)^(n+1) / (n+1) 
 
which is due to 
G.f.: (1/x) * Series_Reversion( x/(1+4*x+x^2) ).  
 
However, the formula from Max seems to be more efficient. 
      Paul 
 
---------- Original Message ----------
From: Max Alekseyev <maxale at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Cc: Karol <penson at lptl.jussieu.fr>
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
Date: Mon, 2 Feb 2015 18:52:29 -0500

Hi Karol,

There is a formula

A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,

which expands (with substitution k -> n-2k) into:

A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
(k+1) * 4^(n-2k)

PARI/GP code:

{ A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
* 4^(n-2*k) ) }

Regards,
Max



On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
> Does anybody know how to obtain the close form of A005572(n) ?
>
> Thanking in advance,
>
>     Karol A. Penson
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/



From hv at crypt.org  Tue Feb  3 18:34:58 2015
From: hv at crypt.org (hv at crypt.org)
Date: Tue, 03 Feb 2015 17:34:58 +0000
Subject: [seqfan] A113917 and A113918: zero-free squaring
Message-ID: <201502031734.t13HYwP09486@crypt.org>

Back in Jan 2006, David Wilson introduced this question:

  For a number n, let f(n) be the set of numbers gotten by splitting n^2 at
  the 0 digits.  For example

  29648^2 = 879003904

  so f(29648) = { 4, 39, 879 }

  Let S be the smallest set of numbers containing 2 and fixed by f.  What is
  the largest element of S?

.. which eventually gave A113917 (largest element) and A113918 (cardinality
of the set).

I did say at the time "I don't have full confidence in the results", but
when trying to clean up my 2006 code recently, as part of a long-running
project to push all my maths code to Github, I found several bugs which
meant some of the results were wrong. Sorry about that.

I've fixed those and further improved the code, available under 'zerofree'
in <https://github.com/hvds/seq>, and will go update the sequences on
the assumption that my new code is correct. I'd still appreciate it if
someone could confirm some or all of the values though.

I estimate the cardinality for A113918(9) is between 10^10 and 10^13,
which I can't calculate with my current approach (but I have another
approach in mind that might reach it). Given the rate of growth, I think
n=10 (ie the original question) is likely to be beyond my means.

With the new code it's easy to change the calculation, and replacing
s -> s^2 with s -> 2s gives a new pair of sequences that grows slow enough
it's easy to calculate more terms; I'm not sure if they're also worth
adding to OEIS, or if there are different calculations that would also be
of interest.

Hugo
---
With calculation s -> s^2: "n: card(n) max(n)"
2: 2 2
3: 18 1849
4: 2 2
5: 3050 266423227914725931
6: 34762 3100840870711697060720215047
7: 3087549 845486430620513036335402848567278325780455810752216401
8: 2 4

With calculation s -> 2s: "n: card(n) max(n)"
2: 2 2
3: 6 16
4: 2 2
5: 20 192
6: 13 128
7: 72 32768
8: 3 4
9: 92 69632
10: 42 23552
11: 308 25722880
12: 34 425984
13: 900 717895680
14: 178 1051828224
15: 1739 217079873536
16: 4 8
17: 3349 2270641389568
18: 443 10603200512
19: 4523 156423849771008
20: 387 950175531008
21: 14364 25160124578398208
22: 1827 385584983965696
23: 18672 450589122059304960
24: 234 40722497536
25: 39426 53279734579488838656
26: 15882 127148822502119047168
27: 52664 299326717942059499520
28: 8858 43157851113903387312128
29: 128253 13526981441472537034752
30: 28346 449522648486053412864
31: 123087 371244129204723018366976
32: 5 16
33: 259207 23655711299608586448011264
34: 87797 103182870656711001112576
35: 363512 39823687474383259120435200
36: 44545 63973308447624725004288
37: 671389 313519863989706816307303809024
38: 182549 45225850656203876163438682112
39: 1336282 31933986316064959928909955072
40: 18049 6034750858947540643601186816
41: 1289210 4145806855637690163777954119680
42: 634402 143410752413726318705389116325888
43: 2679419 251570201273324198920857495653056512
44: 156629 9442738596003761319219036160
45: 3428818 288049927140258932406824739012608
46: 987498 20384387023837630566380055072075677696
47: 5876576 16579286652350303184601394767032483840
48: 13308 152556272234873601963528260943872
49: 8122478 463424116819682991065891465214793542008832
50: 3118809 63039435236897106221986787164071919616
51: 14743535 247126135557931098912701316497011638272
52: 796352 1083181655178944127338714024967634157568
53: 15921180 71286088956163866149580753955553592475648
54: 4952057 2150676694930424720837752491965232971776
55: 29170111 507477067298501219491044453334717130866688
56: 403964 1746977513106742264740052226757623808
57: 48839762 27320774362755367988623371083844092646391808
58: 11997500 6094365163190490383475585992644805477269504
59: 71116907 9188495794580645540482153719631435565136609280
60: 2675259 14463684581762047084433709884282673037312
61: 122451245 9107655699502841924691980127153411750800769679360
62: 17820844 199082515611433949561498862265902993781030912



From njasloane at gmail.com  Wed Feb  4 01:33:51 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 3 Feb 2015 19:33:51 -0500
Subject: [seqfan] Re: A113917 and A113918: zero-free squaring
In-Reply-To: <201502031734.t13HYwP09486@crypt.org>
References: <201502031734.t13HYwP09486@crypt.org>
Message-ID: <CAAOnSgRCE4f0Bj5ADpt2nQjufdYz_j_69E+vaVp_SbJm85O4SA@mail.gmail.com>

Hans, certainly those two sequences are worth adding
to the OEIS! Please do so!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Feb 3, 2015 at 12:34 PM, <hv at crypt.org> wrote:

> Back in Jan 2006, David Wilson introduced this question:
>
>   For a number n, let f(n) be the set of numbers gotten by splitting n^2 at
>   the 0 digits.  For example
>
>   29648^2 = 879003904
>
>   so f(29648) = { 4, 39, 879 }
>
>   Let S be the smallest set of numbers containing 2 and fixed by f.  What
> is
>   the largest element of S?
>
> .. which eventually gave A113917 (largest element) and A113918 (cardinality
> of the set).
>
> I did say at the time "I don't have full confidence in the results", but
> when trying to clean up my 2006 code recently, as part of a long-running
> project to push all my maths code to Github, I found several bugs which
> meant some of the results were wrong. Sorry about that.
>
> I've fixed those and further improved the code, available under 'zerofree'
> in <https://github.com/hvds/seq>, and will go update the sequences on
> the assumption that my new code is correct. I'd still appreciate it if
> someone could confirm some or all of the values though.
>
> I estimate the cardinality for A113918(9) is between 10^10 and 10^13,
> which I can't calculate with my current approach (but I have another
> approach in mind that might reach it). Given the rate of growth, I think
> n=10 (ie the original question) is likely to be beyond my means.
>
> With the new code it's easy to change the calculation, and replacing
> s -> s^2 with s -> 2s gives a new pair of sequences that grows slow enough
> it's easy to calculate more terms; I'm not sure if they're also worth
> adding to OEIS, or if there are different calculations that would also be
> of interest.
>
> Hugo
> ---
> With calculation s -> s^2: "n: card(n) max(n)"
> 2: 2 2
> 3: 18 1849
> 4: 2 2
> 5: 3050 266423227914725931
> 6: 34762 3100840870711697060720215047
> 7: 3087549 845486430620513036335402848567278325780455810752216401
> 8: 2 4
>
> With calculation s -> 2s: "n: card(n) max(n)"
> 2: 2 2
> 3: 6 16
> 4: 2 2
> 5: 20 192
> 6: 13 128
> 7: 72 32768
> 8: 3 4
> 9: 92 69632
> 10: 42 23552
> 11: 308 25722880
> 12: 34 425984
> 13: 900 717895680
> 14: 178 1051828224
> 15: 1739 217079873536
> 16: 4 8
> 17: 3349 2270641389568
> 18: 443 10603200512
> 19: 4523 156423849771008
> 20: 387 950175531008
> 21: 14364 25160124578398208
> 22: 1827 385584983965696
> 23: 18672 450589122059304960
> 24: 234 40722497536
> 25: 39426 53279734579488838656
> 26: 15882 127148822502119047168
> 27: 52664 299326717942059499520
> 28: 8858 43157851113903387312128
> 29: 128253 13526981441472537034752
> 30: 28346 449522648486053412864
> 31: 123087 371244129204723018366976
> 32: 5 16
> 33: 259207 23655711299608586448011264
> 34: 87797 103182870656711001112576
> 35: 363512 39823687474383259120435200
> 36: 44545 63973308447624725004288
> 37: 671389 313519863989706816307303809024
> 38: 182549 45225850656203876163438682112
> 39: 1336282 31933986316064959928909955072
> 40: 18049 6034750858947540643601186816
> 41: 1289210 4145806855637690163777954119680
> 42: 634402 143410752413726318705389116325888
> 43: 2679419 251570201273324198920857495653056512
> 44: 156629 9442738596003761319219036160
> 45: 3428818 288049927140258932406824739012608
> 46: 987498 20384387023837630566380055072075677696
> 47: 5876576 16579286652350303184601394767032483840
> 48: 13308 152556272234873601963528260943872
> 49: 8122478 463424116819682991065891465214793542008832
> 50: 3118809 63039435236897106221986787164071919616
> 51: 14743535 247126135557931098912701316497011638272
> 52: 796352 1083181655178944127338714024967634157568
> 53: 15921180 71286088956163866149580753955553592475648
> 54: 4952057 2150676694930424720837752491965232971776
> 55: 29170111 507477067298501219491044453334717130866688
> 56: 403964 1746977513106742264740052226757623808
> 57: 48839762 27320774362755367988623371083844092646391808
> 58: 11997500 6094365163190490383475585992644805477269504
> 59: 71116907 9188495794580645540482153719631435565136609280
> 60: 2675259 14463684581762047084433709884282673037312
> 61: 122451245 9107655699502841924691980127153411750800769679360
> 62: 17820844 199082515611433949561498862265902993781030912
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Wed Feb  4 01:36:17 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 3 Feb 2015 19:36:17 -0500
Subject: [seqfan] Re: A113917 and A113918: zero-free squaring
In-Reply-To: <CAAOnSgRCE4f0Bj5ADpt2nQjufdYz_j_69E+vaVp_SbJm85O4SA@mail.gmail.com>
References: <201502031734.t13HYwP09486@crypt.org>
 <CAAOnSgRCE4f0Bj5ADpt2nQjufdYz_j_69E+vaVp_SbJm85O4SA@mail.gmail.com>
Message-ID: <CAAOnSgQL8D43Hw1c3Rvy6O88Y36ba1cG=5Eh2AcntidgNRgdQw@mail.gmail.com>

Hugo, Is what I meant to say...

Hugo,   certainly those two sequences are worth adding
to the OEIS! Please do so!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Feb 3, 2015 at 7:33 PM, Neil Sloane <njasloane at gmail.com> wrote:

> Hans, certainly those two sequences are worth adding
> to the OEIS! Please do so!
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Tue, Feb 3, 2015 at 12:34 PM, <hv at crypt.org> wrote:
>
>> Back in Jan 2006, David Wilson introduced this question:
>>
>>   For a number n, let f(n) be the set of numbers gotten by splitting n^2
>> at
>>   the 0 digits.  For example
>>
>>   29648^2 = 879003904
>>
>>   so f(29648) = { 4, 39, 879 }
>>
>>   Let S be the smallest set of numbers containing 2 and fixed by f.  What
>> is
>>   the largest element of S?
>>
>> .. which eventually gave A113917 (largest element) and A113918
>> (cardinality
>> of the set).
>>
>> I did say at the time "I don't have full confidence in the results", but
>> when trying to clean up my 2006 code recently, as part of a long-running
>> project to push all my maths code to Github, I found several bugs which
>> meant some of the results were wrong. Sorry about that.
>>
>> I've fixed those and further improved the code, available under 'zerofree'
>> in <https://github.com/hvds/seq>, and will go update the sequences on
>> the assumption that my new code is correct. I'd still appreciate it if
>> someone could confirm some or all of the values though.
>>
>> I estimate the cardinality for A113918(9) is between 10^10 and 10^13,
>> which I can't calculate with my current approach (but I have another
>> approach in mind that might reach it). Given the rate of growth, I think
>> n=10 (ie the original question) is likely to be beyond my means.
>>
>> With the new code it's easy to change the calculation, and replacing
>> s -> s^2 with s -> 2s gives a new pair of sequences that grows slow enough
>> it's easy to calculate more terms; I'm not sure if they're also worth
>> adding to OEIS, or if there are different calculations that would also be
>> of interest.
>>
>> Hugo
>> ---
>> With calculation s -> s^2: "n: card(n) max(n)"
>> 2: 2 2
>> 3: 18 1849
>> 4: 2 2
>> 5: 3050 266423227914725931
>> 6: 34762 3100840870711697060720215047
>> 7: 3087549 845486430620513036335402848567278325780455810752216401
>> 8: 2 4
>>
>> With calculation s -> 2s: "n: card(n) max(n)"
>> 2: 2 2
>> 3: 6 16
>> 4: 2 2
>> 5: 20 192
>> 6: 13 128
>> 7: 72 32768
>> 8: 3 4
>> 9: 92 69632
>> 10: 42 23552
>> 11: 308 25722880
>> 12: 34 425984
>> 13: 900 717895680
>> 14: 178 1051828224
>> 15: 1739 217079873536
>> 16: 4 8
>> 17: 3349 2270641389568
>> 18: 443 10603200512
>> 19: 4523 156423849771008
>> 20: 387 950175531008
>> 21: 14364 25160124578398208
>> 22: 1827 385584983965696
>> 23: 18672 450589122059304960
>> 24: 234 40722497536
>> 25: 39426 53279734579488838656
>> 26: 15882 127148822502119047168
>> 27: 52664 299326717942059499520
>> 28: 8858 43157851113903387312128
>> 29: 128253 13526981441472537034752
>> 30: 28346 449522648486053412864
>> 31: 123087 371244129204723018366976
>> 32: 5 16
>> 33: 259207 23655711299608586448011264
>> 34: 87797 103182870656711001112576
>> 35: 363512 39823687474383259120435200
>> 36: 44545 63973308447624725004288
>> 37: 671389 313519863989706816307303809024
>> 38: 182549 45225850656203876163438682112
>> 39: 1336282 31933986316064959928909955072
>> 40: 18049 6034750858947540643601186816
>> 41: 1289210 4145806855637690163777954119680
>> 42: 634402 143410752413726318705389116325888
>> 43: 2679419 251570201273324198920857495653056512
>> 44: 156629 9442738596003761319219036160
>> 45: 3428818 288049927140258932406824739012608
>> 46: 987498 20384387023837630566380055072075677696
>> 47: 5876576 16579286652350303184601394767032483840
>> 48: 13308 152556272234873601963528260943872
>> 49: 8122478 463424116819682991065891465214793542008832
>> 50: 3118809 63039435236897106221986787164071919616
>> 51: 14743535 247126135557931098912701316497011638272
>> 52: 796352 1083181655178944127338714024967634157568
>> 53: 15921180 71286088956163866149580753955553592475648
>> 54: 4952057 2150676694930424720837752491965232971776
>> 55: 29170111 507477067298501219491044453334717130866688
>> 56: 403964 1746977513106742264740052226757623808
>> 57: 48839762 27320774362755367988623371083844092646391808
>> 58: 11997500 6094365163190490383475585992644805477269504
>> 59: 71116907 9188495794580645540482153719631435565136609280
>> 60: 2675259 14463684581762047084433709884282673037312
>> 61: 122451245 9107655699502841924691980127153411750800769679360
>> 62: 17820844 199082515611433949561498862265902993781030912
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>


From hv at crypt.org  Wed Feb  4 02:52:19 2015
From: hv at crypt.org (hv at crypt.org)
Date: Wed, 04 Feb 2015 01:52:19 +0000
Subject: [seqfan] Re: A113917 and A113918: zero-free squaring
In-Reply-To: <CAAOnSgQL8D43Hw1c3Rvy6O88Y36ba1cG=5Eh2AcntidgNRgdQw@mail.gmail.com> 
Message-ID: <201502040152.t141qJP10329@crypt.org>

Now proposed as A254637, A254638.

(Given it's otherwise the same code as discussed below for A113917/8, maybe
this would be a better example for someone else to confirm.)

Hugo

Neil Sloane <njasloane at gmail.com> wrote:
:Hugo, Is what I meant to say...
:
:Hugo,   certainly those two sequences are worth adding
:to the OEIS! Please do so!
:
:Best regards
:Neil
:
:Neil J. A. Sloane, President, OEIS Foundation.
:11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
:Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
:Phone: 732 828 6098; home page: http://NeilSloane.com
:Email: njasloane at gmail.com
:
:
:On Tue, Feb 3, 2015 at 7:33 PM, Neil Sloane <njasloane at gmail.com> wrote:
:
:> Hans, certainly those two sequences are worth adding
:> to the OEIS! Please do so!
:>
:> Best regards
:> Neil
:>
:> Neil J. A. Sloane, President, OEIS Foundation.
:> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
:> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
:> Phone: 732 828 6098; home page: http://NeilSloane.com
:> Email: njasloane at gmail.com
:>
:>
:> On Tue, Feb 3, 2015 at 12:34 PM, <hv at crypt.org> wrote:
:>
:>> Back in Jan 2006, David Wilson introduced this question:
:>>
:>>   For a number n, let f(n) be the set of numbers gotten by splitting n^2
:>> at
:>>   the 0 digits.  For example
:>>
:>>   29648^2 = 879003904
:>>
:>>   so f(29648) = { 4, 39, 879 }
:>>
:>>   Let S be the smallest set of numbers containing 2 and fixed by f.  What
:>> is
:>>   the largest element of S?
:>>
:>> .. which eventually gave A113917 (largest element) and A113918
:>> (cardinality
:>> of the set).
:>>
:>> I did say at the time "I don't have full confidence in the results", but
:>> when trying to clean up my 2006 code recently, as part of a long-running
:>> project to push all my maths code to Github, I found several bugs which
:>> meant some of the results were wrong. Sorry about that.
:>>
:>> I've fixed those and further improved the code, available under 'zerofree'
:>> in <https://github.com/hvds/seq>, and will go update the sequences on
:>> the assumption that my new code is correct. I'd still appreciate it if
:>> someone could confirm some or all of the values though.
:>>
:>> I estimate the cardinality for A113918(9) is between 10^10 and 10^13,
:>> which I can't calculate with my current approach (but I have another
:>> approach in mind that might reach it). Given the rate of growth, I think
:>> n=10 (ie the original question) is likely to be beyond my means.
:>>
:>> With the new code it's easy to change the calculation, and replacing
:>> s -> s^2 with s -> 2s gives a new pair of sequences that grows slow enough
:>> it's easy to calculate more terms; I'm not sure if they're also worth
:>> adding to OEIS, or if there are different calculations that would also be
:>> of interest.
:>>
:>> Hugo
:>> ---
:>> With calculation s -> s^2: "n: card(n) max(n)"
:>> 2: 2 2
:>> 3: 18 1849
:>> 4: 2 2
:>> 5: 3050 266423227914725931
:>> 6: 34762 3100840870711697060720215047
:>> 7: 3087549 845486430620513036335402848567278325780455810752216401
:>> 8: 2 4
:>>
:>> With calculation s -> 2s: "n: card(n) max(n)"
:>> 2: 2 2
:>> 3: 6 16
:>> 4: 2 2
:>> 5: 20 192
:>> 6: 13 128
:>> 7: 72 32768
:>> 8: 3 4
:>> 9: 92 69632
:>> 10: 42 23552
:>> 11: 308 25722880
:>> 12: 34 425984
:>> 13: 900 717895680
:>> 14: 178 1051828224
:>> 15: 1739 217079873536
:>> 16: 4 8
:>> 17: 3349 2270641389568
:>> 18: 443 10603200512
:>> 19: 4523 156423849771008
:>> 20: 387 950175531008
:>> 21: 14364 25160124578398208
:>> 22: 1827 385584983965696
:>> 23: 18672 450589122059304960
:>> 24: 234 40722497536
:>> 25: 39426 53279734579488838656
:>> 26: 15882 127148822502119047168
:>> 27: 52664 299326717942059499520
:>> 28: 8858 43157851113903387312128
:>> 29: 128253 13526981441472537034752
:>> 30: 28346 449522648486053412864
:>> 31: 123087 371244129204723018366976
:>> 32: 5 16
:>> 33: 259207 23655711299608586448011264
:>> 34: 87797 103182870656711001112576
:>> 35: 363512 39823687474383259120435200
:>> 36: 44545 63973308447624725004288
:>> 37: 671389 313519863989706816307303809024
:>> 38: 182549 45225850656203876163438682112
:>> 39: 1336282 31933986316064959928909955072
:>> 40: 18049 6034750858947540643601186816
:>> 41: 1289210 4145806855637690163777954119680
:>> 42: 634402 143410752413726318705389116325888
:>> 43: 2679419 251570201273324198920857495653056512
:>> 44: 156629 9442738596003761319219036160
:>> 45: 3428818 288049927140258932406824739012608
:>> 46: 987498 20384387023837630566380055072075677696
:>> 47: 5876576 16579286652350303184601394767032483840
:>> 48: 13308 152556272234873601963528260943872
:>> 49: 8122478 463424116819682991065891465214793542008832
:>> 50: 3118809 63039435236897106221986787164071919616
:>> 51: 14743535 247126135557931098912701316497011638272
:>> 52: 796352 1083181655178944127338714024967634157568
:>> 53: 15921180 71286088956163866149580753955553592475648
:>> 54: 4952057 2150676694930424720837752491965232971776
:>> 55: 29170111 507477067298501219491044453334717130866688
:>> 56: 403964 1746977513106742264740052226757623808
:>> 57: 48839762 27320774362755367988623371083844092646391808
:>> 58: 11997500 6094365163190490383475585992644805477269504
:>> 59: 71116907 9188495794580645540482153719631435565136609280
:>> 60: 2675259 14463684581762047084433709884282673037312
:>> 61: 122451245 9107655699502841924691980127153411750800769679360
:>> 62: 17820844 199082515611433949561498862265902993781030912
:>>
:>>
:>> _______________________________________________
:>>
:>> Seqfan Mailing list - http://list.seqfan.eu/
:>>
:>
:>
:
:_______________________________________________
:
:Seqfan Mailing list - http://list.seqfan.eu/


From maxale at gmail.com  Wed Feb  4 03:06:14 2015
From: maxale at gmail.com (Max Alekseyev)
Date: Tue, 3 Feb 2015 21:06:14 -0500
Subject: [seqfan] self-referential forms
Message-ID: <CAJkPp5PBaxzLRz51L27YevxjnG90HW1cKM1Fg2FoW2vfBGK6dA@mail.gmail.com>

SeqFans,

I've recently tried to formalize and give some counts for the question
on self-referential forms at MathOverflow:
http://mathoverflow.net/questions/194905/compiling-self-referential-forms
In particular, I computed two sequences there, which may be considered
for addition to the OIES.
I'm however not sure if they are motivated enough and not too special
for the general interest. So I'd like to know your opinion in this
respect.

Regards,
Max


From njasloane at gmail.com  Wed Feb  4 04:03:31 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 3 Feb 2015 22:03:31 -0500
Subject: [seqfan] Re: self-referential forms
In-Reply-To: <CAJkPp5PBaxzLRz51L27YevxjnG90HW1cKM1Fg2FoW2vfBGK6dA@mail.gmail.com>
References: <CAJkPp5PBaxzLRz51L27YevxjnG90HW1cKM1Fg2FoW2vfBGK6dA@mail.gmail.com>
Message-ID: <CAAOnSgQ-zd7NBNqzikasoFpW9Rz7Dz7La1t28nf3hNLEWG82rg@mail.gmail.com>

Max, Those sequences have 3 things going for them
- they were created by one of the best contributors
to the OEIS (you), they are on the web, and at least one
other person on math overflow is interested in them.

So, yes, definitely submit them

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Feb 3, 2015 at 9:06 PM, Max Alekseyev <maxale at gmail.com> wrote:

> SeqFans,
>
> I've recently tried to formalize and give some counts for the question
> on self-referential forms at MathOverflow:
> http://mathoverflow.net/questions/194905/compiling-self-referential-forms
> In particular, I computed two sequences there, which may be considered
> for addition to the OIES.
> I'm however not sure if they are motivated enough and not too special
> for the general interest. So I'd like to know your opinion in this
> respect.
>
> Regards,
> Max
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From ixitol at gmail.com  Wed Feb  4 06:33:57 2015
From: ixitol at gmail.com (Russell Walsmith)
Date: Tue, 3 Feb 2015 21:33:57 -0800
Subject: [seqfan] A sequence of sequence-generating matrices
Message-ID: <CAOPCv-XEsNTn_dv=5kTyc-J5K-t0C=ZpeNEz8k2=Fy9DOhNW+Q@mail.gmail.com>

Exploring different numerical sequences* generated by a certain 3 x 3
matrix, I found it to be part of an n x n family with a similar, though
increasingly complex, form. I've discovered six entries in this sequence of
matrices so far... does anyone see where it goes from here...?

http://ixitol.com/MatrixSequence

* (e.g., A249578 <https://oeis.org/A249578>, A249579
<https://oeis.org/A249579>, A249580 <https://oeis.org/A249580>...)


From penson at lptmc.jussieu.fr  Wed Feb  4 20:01:38 2015
From: penson at lptmc.jussieu.fr (Karol A. Penson)
Date: Wed, 04 Feb 2015 20:01:38 +0100
Subject: [seqfan]  Re: Question on A005572 from K. A. Penson
In-Reply-To: <Prayer.1.3.5.1502021746310.15725@viol.math.ubc.ca>
References: <54D00718.50007@lptl.jussieu.fr>
 <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>
 <Prayer.1.3.5.1502021746310.15725@viol.math.ubc.ca>
Message-ID: <54D26C92.9040708@lptmc.jussieu.fr>

  Re: A005572

I thank Max Alekseyev, Robert Israel and Paul Hanna for important remarks.
Robert's compact form can be further transformed using formula 
8.3.2.135, ch.8, p.666
  of  Yury A. Brychkov, "Handbook of Special Functions, Derivatives, 
Integrals, Series and Other Formulas",
(CRC Press, Taylor and Francis, New York, 2008),
and the following relation obtains using  the classical Gegenbauer 
polynomials, in Maple notation:

  A005572(n)=2*(12^(n/2))*(n!/(n+2)!)*GegenbauerC(n, 3/2, 2/sqrt(3)), 
n=0,1... .

Robert, would you like to enter your formula; I will then enter my 
Gegenbauer version.

Best,


Karol A. Penson






Le 03/02/2015 02:46, israel at math.ubc.ca a ?crit :
> And, according to Maple, these sums can be written as a hypergeometric 
> function:
>
> A005572(n) = 4^n*hypergeom([-n/2, (1-n)/2], [2], 1/4)
>
> Cheers,
> Robert
>
> On Feb 2 2015, Max Alekseyev wrote:
>
>> Hi Karol,
>>
>> There is a formula
>>
>> A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,
>>
>> which expands (with substitution k -> n-2k) into:
>>
>> A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
>> (k+1) * 4^(n-2k)
>>
>> PARI/GP code:
>>
>> { A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
>> * 4^(n-2*k) ) }
>>
>> Regards,
>> Max
>>
>>
>>
>> On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
>>> Does anybody know how to obtain the close form of A005572(n) ?
>>>
>>> Thanking in advance,
>>>
>>>     Karol A. Penson
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



From israel at math.ubc.ca  Wed Feb  4 22:40:06 2015
From: israel at math.ubc.ca (israel at math.ubc.ca)
Date: 04 Feb 2015 13:40:06 -0800
Subject: [seqfan] Re: Question on A005572 from K. A. Penson
In-Reply-To: <54D26C92.9040708@lptmc.jussieu.fr>
References: <54D00718.50007@lptl.jussieu.fr>
 <CAJkPp5N0zSqccbCfPPXfwHuVoz983ftn7Q9kayvz+NBvcrVhuw@mail.gmail.com>
 <Prayer.1.3.5.1502021746310.15725@viol.math.ubc.ca>
 <54D26C92.9040708@lptmc.jussieu.fr>
Message-ID: <Prayer.1.3.5.1502041340060.29479@viol.math.ubc.ca>

Done.  I note that Peter Luschny has also entered a different
hypergeometric form.  I don't know how that one was derived.

Cheers,
Robert

On Feb 4 2015, Karol A. Penson wrote:

>  Re: A005572
>
>I thank Max Alekseyev, Robert Israel and Paul Hanna for important remarks.
>Robert's compact form can be further transformed using formula 
>8.3.2.135, ch.8, p.666
>  of  Yury A. Brychkov, "Handbook of Special Functions, Derivatives, 
>Integrals, Series and Other Formulas",
>(CRC Press, Taylor and Francis, New York, 2008),
>and the following relation obtains using  the classical Gegenbauer 
>polynomials, in Maple notation:
>
>  A005572(n)=2*(12^(n/2))*(n!/(n+2)!)*GegenbauerC(n, 3/2, 2/sqrt(3)), 
>n=0,1... .
>
>Robert, would you like to enter your formula; I will then enter my 
>Gegenbauer version.
>
>Best,
>
>
>Karol A. Penson
>
>
>
>
>
>
>Le 03/02/2015 02:46, israel at math.ubc.ca a ?crit :
>> And, according to Maple, these sums can be written as a hypergeometric 
>> function:
>>
>> A005572(n) = 4^n*hypergeom([-n/2, (1-n)/2], [2], 1/4)
>>
>> Cheers,
>> Robert
>>
>> On Feb 2 2015, Max Alekseyev wrote:
>>
>>> Hi Karol,
>>>
>>> There is a formula
>>>
>>> A005572(n) = \sum_{k=0}^n A097610(n,k)*4^k,
>>>
>>> which expands (with substitution k -> n-2k) into:
>>>
>>> A005572(n) = \sum_{k=0}^{[n/2]} binomial(n,2*k) * binomial(2k,k) /
>>> (k+1) * 4^(n-2k)
>>>
>>> PARI/GP code:
>>>
>>> { A005572(n) = sum(k=0,n\2, binomial(n,2*k) * binomial(2*k,k) / (k+1)
>>> * 4^(n-2*k) ) }
>>>
>>> Regards,
>>> Max
>>>
>>>
>>>
>>> On Mon, Feb 2, 2015 at 6:24 PM, Karol <penson at lptl.jussieu.fr> wrote:
>>>> Does anybody know how to obtain the close form of A005572(n) ?
>>>>
>>>> Thanking in advance,
>>>>
>>>>     Karol A. Penson
>>>>
>>>> _______________________________________________
>>>>
>>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>



From mathar at mpia-hd.mpg.de  Thu Feb  5 20:08:28 2015
From: mathar at mpia-hd.mpg.de (Richard J. Mathar)
Date: Thu, 5 Feb 2015 20:08:28 +0100
Subject: [seqfan] g.f. in A157143
Message-ID: <20150205190828.GA14851@mathar.mpia-hd.mpg.de>

Is the generating function in A157143 correct?
The Maple lines
 cx := (1-sqrt(1-4*x))/(2*x) ;
 gx := subs(x=(x/(1+x^2+x^3))^2,cx)*(1-x)/(1+x^2+x^3) ;
 series(%,x=0,50) ;
 gfun[seriestolist](%) ;

based on the A000108 g.f.  generate
1, -1, 0, -1, 1, -1, 2, -2, 4, -5, 8, -13, 18, -32, 46, -77, 123, -192, 325,..

and the 
 mx := (1-x-sqrt(1-2*x-3*x^2))/(2*x^2) ;
 gx := subs(x=(x/(1+x^2+x^3))^2,mx)*(1-x)/(1+x^2+x^3) ;
 series(%,x=0,50) ;
 gfun[seriestolist](%) ;

based on the A000106 (assuming a typo in the formula) g.f. gives
1, -1, 0, -1, 1, -1, 1, -1, 6, 0, -3, -20, 10, 20, 20, -84, -3, 135, 228
and both don't match.


From rselcoe at entouchonline.net  Sat Feb  7 22:01:47 2015
From: rselcoe at entouchonline.net (Bob Selcoe)
Date: Sat, 7 Feb 2015 15:01:47 -0600
Subject: [seqfan] Question re: A250000
In-Reply-To: <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
References: <9822A525B8DE44D79AD6E4E13405CEB9@OwnerPC>
 <CAAcpPSYqW=bvyWt2Nbm1-67etMVnKEYwQjX0q9DNRNbQ5831JA@mail.gmail.com>
 <54AEBE97.9020305@brennen.net> <88684506471F4A2FA027EEC93A2D771E@OwnerPC>
 <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
Message-ID: <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC>


Hello Seqfans,

The sequence A250000 (maximum number of peacefully coexisting equal-sized 
"armies" of queens on chess boards of varying n X n sizes) poses some 
fascinating problems.

The length of the sequence is small; only up to a(13) = 24.

The "known" lower bound for a solution is a(n) = 9/64*n^2. There is a link 
to a paper by Prestwich and Beck referenced in the sequence which expands on 
this idea.  I can't follow the paper, but it apparently provides an upper 
bound, as well.

For all n = 4m+1 m>=0, I can show a pattern of quasi-symmetric queen 
placement such that a(n) = 2m(m+1).  For m = {0..3}, this is indeed the 
maximum number of queens possible.  For m>=4, these solutions are < the 
known lower bound of (9/64)*n^2.

I have proposed for A250000 examples of solutions using this queen pattern 
for n=9 and n=13.  Please refer to the sequence history to see the pattern. 
Since the pattern yields 40 for n=17, and a(17)=42 is the known lower bound, 
it (apparently) does not provide a solution for a(17).

Can anyone show an actual example of a 17 X 17 chessboard where the number 
of queens > 40, even if it can't be proven to be a solution (maximum number 
of queens) for a(17)?

Best Wishes,
Bob Selcoe
 



From Rob.Pratt at sas.com  Sat Feb  7 23:17:51 2015
From: Rob.Pratt at sas.com (Rob Pratt)
Date: Sat, 7 Feb 2015 22:17:51 +0000
Subject: [seqfan] Re: Question re: A250000
In-Reply-To: <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC>
References: <9822A525B8DE44D79AD6E4E13405CEB9@OwnerPC>
 <CAAcpPSYqW=bvyWt2Nbm1-67etMVnKEYwQjX0q9DNRNbQ5831JA@mail.gmail.com>
 <54AEBE97.9020305@brennen.net> <88684506471F4A2FA027EEC93A2D771E@OwnerPC>
 <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
 <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC>
Message-ID: <f9754f2d350443cab54d2ed30870ac5e@MERCMBX38D.na.SAS.com>

Here's a 17x17 solution with 42 queens of each color:



1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

1

W

W

W

W

W

2

W

W

W

W

W

3

W

W

W

W

W

W

4

W

W

W

W

W

W

5

W

W

W

W

W

W

6

W

W

W

W

W

7

W

W

W

W

8

W

W

W

9

W

W

10

B

B

11

B

B

B

12

B

B

B

B

13

B

B

B

B

B

14

B

B

B

B

B

B

B

15

B

B

B

B

B

B

B

B

16

B

B

B

B

B

B

B

17

B

B

B

B

B

B






-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Bob Selcoe
Sent: Saturday, February 07, 2015 4:02 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Question re: A250000





Hello Seqfans,



The sequence A250000 (maximum number of peacefully coexisting equal-sized "armies" of queens on chess boards of varying n X n sizes) poses some fascinating problems.



The length of the sequence is small; only up to a(13) = 24.



The "known" lower bound for a solution is a(n) = 9/64*n^2. There is a link to a paper by Prestwich and Beck referenced in the sequence which expands on this idea.  I can't follow the paper, but it apparently provides an upper bound, as well.



For all n = 4m+1 m>=0, I can show a pattern of quasi-symmetric queen placement such that a(n) = 2m(m+1).  For m = {0..3}, this is indeed the maximum number of queens possible.  For m>=4, these solutions are < the known lower bound of (9/64)*n^2.



I have proposed for A250000 examples of solutions using this queen pattern for n=9 and n=13.  Please refer to the sequence history to see the pattern.

Since the pattern yields 40 for n=17, and a(17)=42 is the known lower bound, it (apparently) does not provide a solution for a(17).



Can anyone show an actual example of a 17 X 17 chessboard where the number of queens > 40, even if it can't be proven to be a solution (maximum number of queens) for a(17)?



Best Wishes,

Bob Selcoe





_______________________________________________



Seqfan Mailing list - http://list.seqfan.eu/

From Eric.Angelini at kntv.be  Sat Feb  7 23:23:29 2015
From: Eric.Angelini at kntv.be (Eric Angelini)
Date: Sat, 7 Feb 2015 23:23:29 +0100
Subject: [seqfan] Absolute diff and sums not to be shared
Message-ID: <8B00BFBA136BAB43AD27F9EDC3758F03B571C46625@KNTVSRV01.kntv.local>

Hello SeqFans,
We want S to be a permutation of the integers >0;
We want S to be the lexicographically first seq of its kind (see below);
If we take two adjacent integers of S, say p & q, we want that:
-> no other pair of adjacent integers in S shares the abs. diff. |p-q|
-> no other pair of adjacent integers in S shares the sum (p+q)
-> no |p-q|=(p'+q') with p'and q' being two other adjacent integers in S.

So S is extended with the smallest integer n such that neither |(n-1)-n|
nor [(n-1)+n] has occurred before as a sum or as a diff. of two adjacent
integers in S.

  Sum  3  6  12 11 13  28  27 32  29 22
S(n)= 1  2  4  8  3  10  18  9  23  6  16 ...
  Dif  1  2  4  5  7   8   9  14  17 10

Hope this is not old hat,
Best,
?.


From reinhard.zumkeller at gmail.com  Sun Feb  8 00:49:11 2015
From: reinhard.zumkeller at gmail.com (Reinhard Zumkeller)
Date: Sun, 8 Feb 2015 00:49:11 +0100
Subject: [seqfan] Re: Absolute diff and sums not to be shared
In-Reply-To: <8B00BFBA136BAB43AD27F9EDC3758F03B571C46625@KNTVSRV01.kntv.local>
References: <8B00BFBA136BAB43AD27F9EDC3758F03B571C46625@KNTVSRV01.kntv.local>
Message-ID: <CAOyfccivTmKye4LLgwHcyC4_mQoS5wZhbZ9Xs7xTR3kJm4tSwA@mail.gmail.com>

see https://oeis.org/draft/A254788

Best, Reinhard

2015-02-07 23:23 GMT+01:00 Eric Angelini <Eric.Angelini at kntv.be>:

> Hello SeqFans,
> We want S to be a permutation of the integers >0;
> We want S to be the lexicographically first seq of its kind (see below);
> If we take two adjacent integers of S, say p & q, we want that:
> -> no other pair of adjacent integers in S shares the abs. diff. |p-q|
> -> no other pair of adjacent integers in S shares the sum (p+q)
> -> no |p-q|=(p'+q') with p'and q' being two other adjacent integers in S.
>
> So S is extended with the smallest integer n such that neither |(n-1)-n|
> nor [(n-1)+n] has occurred before as a sum or as a diff. of two adjacent
> integers in S.
>
>   Sum  3  6  12 11 13  28  27 32  29 22
> S(n)= 1  2  4  8  3  10  18  9  23  6  16 ...
>   Dif  1  2  4  5  7   8   9  14  17 10
>
> Hope this is not old hat,
> Best,
> ?.
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From Rob.Pratt at sas.com  Sun Feb  8 04:43:30 2015
From: Rob.Pratt at sas.com (Rob Pratt)
Date: Sun, 8 Feb 2015 03:43:30 +0000
Subject: [seqfan] Re: Question re: A250000
References: <9822A525B8DE44D79AD6E4E13405CEB9@OwnerPC>
 <CAAcpPSYqW=bvyWt2Nbm1-67etMVnKEYwQjX0q9DNRNbQ5831JA@mail.gmail.com>
 <54AEBE97.9020305@brennen.net> <88684506471F4A2FA027EEC93A2D771E@OwnerPC>
 <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
 <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC> 
Message-ID: <bf66abc63f7045e49bff4526b491108e@MERCMBX38D.na.SAS.com>

Here it is with unoccupied squares indicated with dots (view with a fixed-width font):

....WWWWW........
....WWWWW........
....WWWWW.......W
....WWWW.......WW
....WWW.......WWW
.....W.......WWWW
.............WWWW
.............WWW.
.............WW..
..BB.............
.BBB.............
BBBB.............
BBBB.......B.....
BBBB......BBB....
BBBB.....BBBB....
BBB......BBBB....
BB.......BBBB....

From: Rob Pratt
Sent: Saturday, February 07, 2015 5:18 PM
To: Sequence Fanatics Discussion list
Subject: RE: [seqfan] Question re: A250000


Here's a 17x17 solution with 42 queens of each color:



1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

1

W

W

W

W

W

2

W

W

W

W

W

3

W

W

W

W

W

W

4

W

W

W

W

W

W

5

W

W

W

W

W

W

6

W

W

W

W

W

7

W

W

W

W

8

W

W

W

9

W

W

10

B

B

11

B

B

B

12

B

B

B

B

13

B

B

B

B

B

14

B

B

B

B

B

B

B

15

B

B

B

B

B

B

B

B

16

B

B

B

B

B

B

B

17

B

B

B

B

B

B






-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Bob Selcoe
Sent: Saturday, February 07, 2015 4:02 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Question re: A250000





Hello Seqfans,



The sequence A250000 (maximum number of peacefully coexisting equal-sized "armies" of queens on chess boards of varying n X n sizes) poses some fascinating problems.



The length of the sequence is small; only up to a(13) = 24.



The "known" lower bound for a solution is a(n) = 9/64*n^2. There is a link to a paper by Prestwich and Beck referenced in the sequence which expands on this idea.  I can't follow the paper, but it apparently provides an upper bound, as well.



For all n = 4m+1 m>=0, I can show a pattern of quasi-symmetric queen placement such that a(n) = 2m(m+1).  For m = {0..3}, this is indeed the maximum number of queens possible.  For m>=4, these solutions are < the known lower bound of (9/64)*n^2.



I have proposed for A250000 examples of solutions using this queen pattern for n=9 and n=13.  Please refer to the sequence history to see the pattern.

Since the pattern yields 40 for n=17, and a(17)=42 is the known lower bound, it (apparently) does not provide a solution for a(17).



Can anyone show an actual example of a 17 X 17 chessboard where the number of queens > 40, even if it can't be proven to be a solution (maximum number of queens) for a(17)?



Best Wishes,

Bob Selcoe







_______________________________________________



Seqfan Mailing list - http://list.seqfan.eu/

From rselcoe at entouchonline.net  Sun Feb  8 07:52:14 2015
From: rselcoe at entouchonline.net (Bob Selcoe)
Date: Sun, 8 Feb 2015 00:52:14 -0600
Subject: [seqfan] Re: Question re: A250000
In-Reply-To: <bf66abc63f7045e49bff4526b491108e@MERCMBX38D.na.SAS.com>
References: <9822A525B8DE44D79AD6E4E13405CEB9@OwnerPC>
 <CAAcpPSYqW=bvyWt2Nbm1-67etMVnKEYwQjX0q9DNRNbQ5831JA@mail.gmail.com>
 <54AEBE97.9020305@brennen.net> <88684506471F4A2FA027EEC93A2D771E@OwnerPC>
 <8D1F9DFE915F766-83C-DC319@webmail-va113.sysops.aol.com>
 <DC3BB0D7AE654FC3ACB814AE749CA734@OwnerPC>
 <bf66abc63f7045e49bff4526b491108e@MERCMBX38D.na.SAS.com>
Message-ID: <EB99758CBECB48E9A1DC4FFB6FC6C060@OwnerPC>

Hi again Rob an others,

And  two more 42-queen variations for n=17:

Alternative 1:

.....WWWWW.......
.....WWWWW.......
.....WWWWW......W
.....WWWW......WW
.....WWW......WWW
......W......WWWW
.............WWWW
.............WWW.
.............WW..
...BB............
..BBB............
.BBBB............
BBBBB......BB....
BBBBB.....BBB....
BBBB......BBB....
BBB.......BBB....
BB........BBB....



Alternative 2:

....WWWW........W
....WWWW.......WW
....WWWW......WWW
....WWWW.....WWWW
.....WW......WWWW
.............WWWW
.............WWW.
.............WW..
.............W...
..BB.............
.BBB.............
BBBB.......B.....
BBBB......BBB....
BBB......BBBB....
BB......BBBBB....
B.......BBBBB....
........BBBBB....


The symmetry of the W-blocks and the quasi-symmetry of the B-blocks for the 
second example surprises me.

I wonder if there are any solutions for a(n) > floor_(9n^2/64) for any n?

Cheers,
Bob S


--------------------------------------------------
From: "Rob Pratt" <Rob.Pratt at sas.com>
Sent: Saturday, February 07, 2015 9:43 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Question re: A250000

> Here it is with unoccupied squares indicated with dots (view with a 
> fixed-width font):
>
> ....WWWWW........
> ....WWWWW........
> ....WWWWW.......W
> ....WWWW.......WW
> ....WWW.......WWW
> .....W.......WWWW
> .............WWWW
> .............WWW.
> .............WW..
> ..BB.............
> .BBB.............
> BBBB.............
> BBBB.......B.....
> BBBB......BBB....
> BBBB.....BBBB....
> BBB......BBBB....
> BB.......BBBB....
>
> From: Rob Pratt
> Sent: Saturday, February 07, 2015 5:18 PM
> To: Sequence Fanatics Discussion list
> Subject: RE: [seqfan] Question re: A250000
>
>
> Here's a 17x17 solution with 42 queens of each color:
>
>
>
> 1
>
> 2
>
> 3
>
> 4
>
> 5
>
> 6
>
> 7
>
> 8
>
> 9
>
> 10
>
> 11
>
> 12
>
> 13
>
> 14
>
> 15
>
> 16
>
> 17
>
> 1
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 2
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 3
>
> W
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 4
>
> W
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 5
>
> W
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 6
>
> W
>
> W
>
> W
>
> W
>
> W
>
> 7
>
> W
>
> W
>
> W
>
> W
>
> 8
>
> W
>
> W
>
> W
>
> 9
>
> W
>
> W
>
> 10
>
> B
>
> B
>
> 11
>
> B
>
> B
>
> B
>
> 12
>
> B
>
> B
>
> B
>
> B
>
> 13
>
> B
>
> B
>
> B
>
> B
>
> B
>
> 14
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> 15
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> 16
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
> 17
>
> B
>
> B
>
> B
>
> B
>
> B
>
> B
>
>
>
>
>
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Bob 
> Selcoe
> Sent: Saturday, February 07, 2015 4:02 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Question re: A250000
>
>
>
>
>
> Hello Seqfans,
>
>
>
> The sequence A250000 (maximum number of peacefully coexisting equal-sized 
> "armies" of queens on chess boards of varying n X n sizes) poses some 
> fascinating problems.
>
>
>
> The length of the sequence is small; only up to a(13) = 24.
>
>
>
> The "known" lower bound for a solution is a(n) = 9/64*n^2. There is a link 
> to a paper by Prestwich and Beck referenced in the sequence which expands 
> on this idea.  I can't follow the paper, but it apparently provides an 
> upper bound, as well.
>
>
>
> For all n = 4m+1 m>=0, I can show a pattern of quasi-symmetric queen 
> placement such that a(n) = 2m(m+1).  For m = {0..3}, this is indeed the 
> maximum number of queens possible.  For m>=4, these solutions are < the 
> known lower bound of (9/64)*n^2.
>
>
>
> I have proposed for A250000 examples of solutions using this queen pattern 
> for n=9 and n=13.  Please refer to the sequence history to see the 
> pattern.
>
> Since the pattern yields 40 for n=17, and a(17)=42 is the known lower 
> bound, it (apparently) does not provide a solution for a(17).
>
>
>
> Can anyone show an actual example of a 17 X 17 chessboard where the number 
> of queens > 40, even if it can't be proven to be a solution (maximum 
> number of queens) for a(17)?
>
>
>
> Best Wishes,
>
> Bob Selcoe
>
>
>
>
>
>
>
> _______________________________________________
>
>
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
> 


From andrew.weimholt at gmail.com  Mon Feb  9 10:29:53 2015
From: andrew.weimholt at gmail.com (Andrew Weimholt)
Date: Mon, 9 Feb 2015 01:29:53 -0800
Subject: [seqfan] A027624 initial term
Message-ID: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>

Hi,

I believe the first term of A027624 should be 2, not 1.

The history shows that Eric W. Weisstein was going to make such a
"correction" a while back, but then changed his mind and backed out the
change.

Can anyone offer an explanation?

Andrew


From franktaw at netscape.net  Mon Feb  9 11:12:26 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Mon, 9 Feb 2015 05:12:26 -0500
Subject: [seqfan] Re: A027624 initial term
In-Reply-To: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>
References: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>
Message-ID: <8D212680A1EAF46-13DC-37227@webmail-va003.sysops.aol.com>

There's the fact that the formula in the definition evaluates to 1 for 
n = 0. Why do you think it should be 2?

Franklin T. Adams-Watters

-----Original Message-----
From: Andrew Weimholt <andrew.weimholt at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Mon, Feb 9, 2015 3:29 am
Subject: [seqfan] A027624 initial term


Hi,

I believe the first term of A027624 should be 2, not 1.

The history shows that Eric W. Weisstein was going to make such a
"correction" a while back, but then changed his mind and backed out the
change.

Can anyone offer an explanation?

Andrew

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From franktaw at netscape.net  Mon Feb  9 11:14:12 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Mon, 9 Feb 2015 05:14:12 -0500
Subject: [seqfan] Re: A027624 initial term
In-Reply-To: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>
References: <CAKPToLWMNcYdwmKwyEiBZszTbGM9LRuM268qP0qmsThycFuNyg@mail.gmail.com>
Message-ID: <8D21268490AA7E6-13DC-3722F@webmail-va003.sysops.aol.com>

Sorry, I typed the wrong sequence number. Please ignore my previous 
message.

Franklin T. Adams-Watters

-----Original Message-----
From: Andrew Weimholt <andrew.weimholt at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Mon, Feb 9, 2015 3:29 am
Subject: [seqfan] A027624 initial term


Hi,

I believe the first term of A027624 should be 2, not 1.

The history shows that Eric W. Weisstein was going to make such a
"correction" a while back, but then changed his mind and backed out the
change.

Can anyone offer an explanation?

Andrew

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From peter.luschny at gmail.com  Wed Feb 11 11:30:35 2015
From: peter.luschny at gmail.com (Peter Luschny)
Date: Wed, 11 Feb 2015 11:30:35 +0100
Subject: [seqfan] A marginal observation on some tables of R. H. Hardin
Message-ID: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>

In  A250544, A223069, A250669, A250692
R. H. Hardin gives the empirical recurrence

a(n) = 16*a(n-1)-106*a(n-2)+376*a(n-3)-769*a(n-4)
       +904*a(n-5)-564*a(n-6)+144*a(n-7)

I simply wish to observe that these coefficients are
listed in the ninth row of Peter Bala's A246117.

Peter


From seqfan at hasler.fr  Wed Feb 11 12:48:59 2015
From: seqfan at hasler.fr (M. F. Hasler)
Date: Wed, 11 Feb 2015 07:48:59 -0400
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
Message-ID: <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>

I added your comment in A250544, and also several missing
cross-references to sequences which list the rows/cols.
It would be nice if others could edit related sequences in a similar manner.

Maximilian

On Wed, Feb 11, 2015 at 6:30 AM, Peter Luschny <peter.luschny at gmail.com> wrote:
> In  A250544, A223069, A250669, A250692
> R. H. Hardin gives the empirical recurrence
>
> a(n) = 16*a(n-1)-106*a(n-2)+376*a(n-3)-769*a(n-4)
>        +904*a(n-5)-564*a(n-6)+144*a(n-7)
>
> I simply wish to observe that these coefficients are
> listed in the ninth row of Peter Bala's A246117.
>
> Peter


From rhhardin at att.net  Wed Feb 11 13:05:10 2015
From: rhhardin at att.net (Ron Hardin)
Date: Wed, 11 Feb 2015 04:05:10 -0800
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
Message-ID: <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>

The row/col/diag series always link to the table, so the refs link in the table will find them.

It always seemed like needless clutter to link the other way without a reason beyond existence.  It seems to claim significance beyond that.

The inbound links by contrast say that there are more like this, in this family.

 
rhhardin at mindspring.com
rhhardin at att.net (either)


>________________________________
> From: M. F. Hasler <seqfan at hasler.fr>
>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
>Sent: Wednesday, February 11, 2015 6:48 AM
>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
> 
>
>I added your comment in A250544, and also several missing
>cross-references to sequences which list the rows/cols.
>It would be nice if others could edit related sequences in a similar manner.
>
>Maximilian
>
>


From seqfan at hasler.fr  Wed Feb 11 13:23:03 2015
From: seqfan at hasler.fr (M. F. Hasler)
Date: Wed, 11 Feb 2015 08:23:03 -0400
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
Message-ID: <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>

Ron,

I am also personally against duplicating links (really never
understood why an A-number put somewhere in comment or formula should
be repeated in Xrefs), but it is nonetheless handy to have the links
to the column sequences because else you have to do a search with only
the sequence number in order to find them via the backlink, but often
you come there following a link and not doing a search (and it is
somehow counter-intuitive to copy-paste the number of the sequence
already displayed on the screen again into the search box...).

Also, in the present case there was no link to the tables A250676 and
A250691 with almost identical definition, and they would not pop up
doing a search for the other sequence numbers.

I also agree on the "significance" issue, and it is painfully to have
a bunch of sequence numbers in the Xrefs without knowing why they are
there. But with 2-3 words of explanation or just hints, this is a true
added value, I think.

Maximilian


On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
> The row/col/diag series always link to the table, so the refs link in the table will find them.
>
> It always seemed like needless clutter to link the other way without a reason beyond existence.  It seems to claim significance beyond that.
>
> The inbound links by contrast say that there are more like this, in this family.
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
>>________________________________
>> From: M. F. Hasler <seqfan at hasler.fr>
>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>Sent: Wednesday, February 11, 2015 6:48 AM
>>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>>
>>
>>I added your comment in A250544, and also several missing
>>cross-references to sequences which list the rows/cols.
>>It would be nice if others could edit related sequences in a similar manner.
>>
>>Maximilian
>>
>>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/


From rhhardin at att.net  Wed Feb 11 13:34:33 2015
From: rhhardin at att.net (Ron Hardin)
Date: Wed, 11 Feb 2015 04:34:33 -0800
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
Message-ID: <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>

I agree than any specific case can benefit from two-way links, but not in general.  At least it seems that way to me.


I don't understand the first paragraph problem you describe below.  Clicking "refs" in the header of the table gives you a nice page with all the rows and columns and diagonals expanded for you, as well as any foreign sequence that happens to reference inwards.

 
rhhardin at mindspring.com
rhhardin at att.net (either)


>________________________________
> From: M. F. Hasler <seqfan at hasler.fr>
>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
>Sent: Wednesday, February 11, 2015 7:23 AM
>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
> 
>
>Ron,
>
>I am also personally against duplicating links (really never
>understood why an A-number put somewhere in comment or formula should
>be repeated in Xrefs), but it is nonetheless handy to have the links
>to the column sequences because else you have to do a search with only
>the sequence number in order to find them via the backlink, but often
>you come there following a link and not doing a search (and it is
>somehow counter-intuitive to copy-paste the number of the sequence
>already displayed on the screen again into the search box...).
>
>Also, in the present case there was no link to the tables A250676 and
>A250691 with almost identical definition, and they would not pop up
>doing a search for the other sequence numbers.
>
>I also agree on the "significance" issue, and it is painfully to have
>a bunch of sequence numbers in the Xrefs without knowing why they are
>there. But with 2-3 words of explanation or just hints, this is a true
>added value, I think.
>
>Maximilian
>
>
>On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
>> The row/col/diag series always link to the table, so the refs link in the table will find them.
>>
>> It always seemed like needless clutter to link the other way without a reason beyond existence.  It seems to claim significance beyond that.
>>
>> The inbound links by contrast say that there are more like this, in this family.
>>
>>
>> rhhardin at mindspring.com
>> rhhardin at att.net (either)
>>
>>
>>>________________________________
>>> From: M. F. Hasler <seqfan at hasler.fr>
>>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>>Sent: Wednesday, February 11, 2015 6:48 AM
>>>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>>>
>>>
>>>I added your comment in A250544, and also several missing
>>>cross-references to sequences which list the rows/cols.
>>>It would be nice if others could edit related sequences in a similar manner.
>>>
>>>Maximilian
>>>
>>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>
>


From Eric.Angelini at kntv.be  Wed Feb 11 14:21:52 2015
From: Eric.Angelini at kntv.be (Eric Angelini)
Date: Wed, 11 Feb 2015 14:21:52 +0100
Subject: [seqfan] a(a(n)+a(n+1)) has property X
Message-ID: <8B00BFBA136BAB43AD27F9EDC3758F03BD24CA4FD9@KNTVSRV01.kntv.local>

Hello SeqFans,
S is the lexico-first permutation of the positive integers with the property ? a(a(n)+a(n+1)) is even ?

S = 1, 2, 4, 3, 5, 6, 8, 10, 7, 9, 12, 11, 13, 14, 15, 16, 18, 20, 17, 19, 22, 21, 24, 26, 23, 25, 28, 27, 30, 29, 32, 31, 33, 34, 35, 36, 38, 40, ...

In other words:
a)  take two adjacent integers x and y in S
b)  let (x + y) = z
c)  a(z) is even.
S was extended with the smallest integer not yet in S and not leading to a contradiction.

Testing the formula:
n = 1  2  3  4  5  6  7   8  9  10 11  12  13  14  15  16  17  18  19  20  21  22 ...
S = 1, 2, 4, 3, 5, 6, 8, 10, 7, 9, 12, 11, 13, 14, 15, 16, 18, 20, 17, 19, 22, 21,...

for n=1 then a(1)=1 and a(2)=2 and a(sum) reads a(1+2) reads a(3) which is 4 (even);
for n=2 then a(2)=2 and a(3)=4 and a(sum) reads a(2+4) reads a(6) which is 6 (even);
for n=3 then a(3)=4 and a(4)=3 and a(sum) reads a(4+3) reads a(7) which is 8 (even);
for n=4 then a(4)=3 and a(5)=5 and a(sum) reads a(3+5) reads a(8) which is 10 (even);
... etc.
--------------------------------------------------------------------
Remark #1:
The seq T, where a(a(n)+a(n+1)) is always odd is already in the OEIS:
https://oeis.org/A000027
;-D
But if we force a(1)=2 we then get again a permutation of A000027:

T' = 2, 1, 3, 5, 4, 6, 7, 9, 11, 13, 8, 10, 15, 12, ,14, 17, 16, 19, 18, 21, 23, 20, 22, 25, 27, 29, 31, 24, 26, 28, 33, ...

--------------------------------------------------------------------
Remark #2:
The seq P, where a(a(n)+a(n+1)) is always prime is also a permutation of of A000027:

P = 1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 13, 10, 17, 12, 19, 14, 15, 23, 29, 31, 16, 37, 41, 18, ...

Best,
?.







From njasloane at gmail.com  Wed Feb 11 17:23:16 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 11:23:16 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
Message-ID: <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>

Just to clarify one point:

The rule is that if there is a line anywhere in the entry that
mentions A123456, then Cf. A123456 should also appear in the
cross-references section.

(there are two good reasons: so Russ's code works
properly, and so the user can easily see if A123456 is
referred to anywhere in the entry without having to search through every
line)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net> wrote:

> I agree than any specific case can benefit from two-way links, but not in
> general.  At least it seems that way to me.
>
>
> I don't understand the first paragraph problem you describe below.
> Clicking "refs" in the header of the table gives you a nice page with all
> the rows and columns and diagonals expanded for you, as well as any foreign
> sequence that happens to reference inwards.
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
> >________________________________
> > From: M. F. Hasler <seqfan at hasler.fr>
> >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >Sent: Wednesday, February 11, 2015 7:23 AM
> >Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> Hardin
> >
> >
> >Ron,
> >
> >I am also personally against duplicating links (really never
> >understood why an A-number put somewhere in comment or formula should
> >be repeated in Xrefs), but it is nonetheless handy to have the links
> >to the column sequences because else you have to do a search with only
> >the sequence number in order to find them via the backlink, but often
> >you come there following a link and not doing a search (and it is
> >somehow counter-intuitive to copy-paste the number of the sequence
> >already displayed on the screen again into the search box...).
> >
> >Also, in the present case there was no link to the tables A250676 and
> >A250691 with almost identical definition, and they would not pop up
> >doing a search for the other sequence numbers.
> >
> >I also agree on the "significance" issue, and it is painfully to have
> >a bunch of sequence numbers in the Xrefs without knowing why they are
> >there. But with 2-3 words of explanation or just hints, this is a true
> >added value, I think.
> >
> >Maximilian
> >
> >
> >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
> >> The row/col/diag series always link to the table, so the refs link in
> the table will find them.
> >>
> >> It always seemed like needless clutter to link the other way without a
> reason beyond existence.  It seems to claim significance beyond that.
> >>
> >> The inbound links by contrast say that there are more like this, in
> this family.
> >>
> >>
> >> rhhardin at mindspring.com
> >> rhhardin at att.net (either)
> >>
> >>
> >>>________________________________
> >>> From: M. F. Hasler <seqfan at hasler.fr>
> >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >>>Sent: Wednesday, February 11, 2015 6:48 AM
> >>>Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> Hardin
> >>>
> >>>
> >>>I added your comment in A250544, and also several missing
> >>>cross-references to sequences which list the rows/cols.
> >>>It would be nice if others could edit related sequences in a similar
> manner.
> >>>
> >>>Maximilian
> >>>
> >>>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> >
> >
> >_______________________________________________
> >
> >Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From charles.greathouse at case.edu  Wed Feb 11 20:15:32 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Wed, 11 Feb 2015 14:15:32 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
Message-ID: <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>

What part of Russ' code work improperly when a sequence is in an entry but
not the xref field?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com> wrote:

> Just to clarify one point:
>
> The rule is that if there is a line anywhere in the entry that
> mentions A123456, then Cf. A123456 should also appear in the
> cross-references section.
>
> (there are two good reasons: so Russ's code works
> properly, and so the user can easily see if A123456 is
> referred to anywhere in the entry without having to search through every
> line)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net> wrote:
>
> > I agree than any specific case can benefit from two-way links, but not in
> > general.  At least it seems that way to me.
> >
> >
> > I don't understand the first paragraph problem you describe below.
> > Clicking "refs" in the header of the table gives you a nice page with all
> > the rows and columns and diagonals expanded for you, as well as any
> foreign
> > sequence that happens to reference inwards.
> >
> >
> > rhhardin at mindspring.com
> > rhhardin at att.net (either)
> >
> >
> > >________________________________
> > > From: M. F. Hasler <seqfan at hasler.fr>
> > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > >Sent: Wednesday, February 11, 2015 7:23 AM
> > >Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> > Hardin
> > >
> > >
> > >Ron,
> > >
> > >I am also personally against duplicating links (really never
> > >understood why an A-number put somewhere in comment or formula should
> > >be repeated in Xrefs), but it is nonetheless handy to have the links
> > >to the column sequences because else you have to do a search with only
> > >the sequence number in order to find them via the backlink, but often
> > >you come there following a link and not doing a search (and it is
> > >somehow counter-intuitive to copy-paste the number of the sequence
> > >already displayed on the screen again into the search box...).
> > >
> > >Also, in the present case there was no link to the tables A250676 and
> > >A250691 with almost identical definition, and they would not pop up
> > >doing a search for the other sequence numbers.
> > >
> > >I also agree on the "significance" issue, and it is painfully to have
> > >a bunch of sequence numbers in the Xrefs without knowing why they are
> > >there. But with 2-3 words of explanation or just hints, this is a true
> > >added value, I think.
> > >
> > >Maximilian
> > >
> > >
> > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
> > >> The row/col/diag series always link to the table, so the refs link in
> > the table will find them.
> > >>
> > >> It always seemed like needless clutter to link the other way without a
> > reason beyond existence.  It seems to claim significance beyond that.
> > >>
> > >> The inbound links by contrast say that there are more like this, in
> > this family.
> > >>
> > >>
> > >> rhhardin at mindspring.com
> > >> rhhardin at att.net (either)
> > >>
> > >>
> > >>>________________________________
> > >>> From: M. F. Hasler <seqfan at hasler.fr>
> > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > >>>Sent: Wednesday, February 11, 2015 6:48 AM
> > >>>Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> > Hardin
> > >>>
> > >>>
> > >>>I added your comment in A250544, and also several missing
> > >>>cross-references to sequences which list the rows/cols.
> > >>>It would be nice if others could edit related sequences in a similar
> > manner.
> > >>>
> > >>>Maximilian
> > >>>
> > >>>
> > >>
> > >> _______________________________________________
> > >>
> > >> Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> > >
> > >
> > >
> > >_______________________________________________
> > >
> > >Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Wed Feb 11 20:41:00 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 14:41:00 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
Message-ID: <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>

 I forget.  But the main reason is for humans to be able to see at a glance
what sequences are mentioned.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> What part of Russ' code work improperly when a sequence is in an entry but
> not the xref field?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > Just to clarify one point:
> >
> > The rule is that if there is a line anywhere in the entry that
> > mentions A123456, then Cf. A123456 should also appear in the
> > cross-references section.
> >
> > (there are two good reasons: so Russ's code works
> > properly, and so the user can easily see if A123456 is
> > referred to anywhere in the entry without having to search through every
> > line)
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net> wrote:
> >
> > > I agree than any specific case can benefit from two-way links, but not
> in
> > > general.  At least it seems that way to me.
> > >
> > >
> > > I don't understand the first paragraph problem you describe below.
> > > Clicking "refs" in the header of the table gives you a nice page with
> all
> > > the rows and columns and diagonals expanded for you, as well as any
> > foreign
> > > sequence that happens to reference inwards.
> > >
> > >
> > > rhhardin at mindspring.com
> > > rhhardin at att.net (either)
> > >
> > >
> > > >________________________________
> > > > From: M. F. Hasler <seqfan at hasler.fr>
> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >Sent: Wednesday, February 11, 2015 7:23 AM
> > > >Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> > > Hardin
> > > >
> > > >
> > > >Ron,
> > > >
> > > >I am also personally against duplicating links (really never
> > > >understood why an A-number put somewhere in comment or formula should
> > > >be repeated in Xrefs), but it is nonetheless handy to have the links
> > > >to the column sequences because else you have to do a search with only
> > > >the sequence number in order to find them via the backlink, but often
> > > >you come there following a link and not doing a search (and it is
> > > >somehow counter-intuitive to copy-paste the number of the sequence
> > > >already displayed on the screen again into the search box...).
> > > >
> > > >Also, in the present case there was no link to the tables A250676 and
> > > >A250691 with almost identical definition, and they would not pop up
> > > >doing a search for the other sequence numbers.
> > > >
> > > >I also agree on the "significance" issue, and it is painfully to have
> > > >a bunch of sequence numbers in the Xrefs without knowing why they are
> > > >there. But with 2-3 words of explanation or just hints, this is a true
> > > >added value, I think.
> > > >
> > > >Maximilian
> > > >
> > > >
> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> wrote:
> > > >> The row/col/diag series always link to the table, so the refs link
> in
> > > the table will find them.
> > > >>
> > > >> It always seemed like needless clutter to link the other way
> without a
> > > reason beyond existence.  It seems to claim significance beyond that.
> > > >>
> > > >> The inbound links by contrast say that there are more like this, in
> > > this family.
> > > >>
> > > >>
> > > >> rhhardin at mindspring.com
> > > >> rhhardin at att.net (either)
> > > >>
> > > >>
> > > >>>________________________________
> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> > > Hardin
> > > >>>
> > > >>>
> > > >>>I added your comment in A250544, and also several missing
> > > >>>cross-references to sequences which list the rows/cols.
> > > >>>It would be nice if others could edit related sequences in a similar
> > > manner.
> > > >>>
> > > >>>Maximilian
> > > >>>
> > > >>>
> > > >>
> > > >> _______________________________________________
> > > >>
> > > >> Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >_______________________________________________
> > > >
> > > >Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > > >
> > > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From franktaw at netscape.net  Wed Feb 11 20:56:01 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Wed, 11 Feb 2015 14:56:01 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
Message-ID: <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>

Just as a point of reference, a search for "A000217 -xref:A000217" 
gives 933 matches, out of 2699 that match "A000217".

Franklin T. Adams-Watters

-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Wed, Feb 11, 2015 1:41 pm
Subject: [seqfan] Re: A marginal observation on some tables of R. H. 
Hardin


  I forget.  But the main reason is for humans to be able to see at a 
glance
what sequences are mentioned.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> What part of Russ' code work improperly when a sequence is in an 
entry but
> not the xref field?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com> 
wrote:
>
> > Just to clarify one point:
> >
> > The rule is that if there is a line anywhere in the entry that
> > mentions A123456, then Cf. A123456 should also appear in the
> > cross-references section.
> >
> > (there are two good reasons: so Russ's code works
> > properly, and so the user can easily see if A123456 is
> > referred to anywhere in the entry without having to search through 
every
> > line)
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, 
Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net> 
wrote:
> >
> > > I agree than any specific case can benefit from two-way links, 
but not
> in
> > > general.  At least it seems that way to me.
> > >
> > >
> > > I don't understand the first paragraph problem you describe below.
> > > Clicking "refs" in the header of the table gives you a nice page 
with
> all
> > > the rows and columns and diagonals expanded for you, as well as 
any
> > foreign
> > > sequence that happens to reference inwards.
> > >
> > >
> > > rhhardin at mindspring.com
> > > rhhardin at att.net (either)
> > >
> > >
> > > >________________________________
> > > > From: M. F. Hasler <seqfan at hasler.fr>
> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >Sent: Wednesday, February 11, 2015 7:23 AM
> > > >Subject: [seqfan] Re: A marginal observation on some tables of 
R. H.
> > > Hardin
> > > >
> > > >
> > > >Ron,
> > > >
> > > >I am also personally against duplicating links (really never
> > > >understood why an A-number put somewhere in comment or formula 
should
> > > >be repeated in Xrefs), but it is nonetheless handy to have the 
links
> > > >to the column sequences because else you have to do a search 
with only
> > > >the sequence number in order to find them via the backlink, but 
often
> > > >you come there following a link and not doing a search (and it is
> > > >somehow counter-intuitive to copy-paste the number of the 
sequence
> > > >already displayed on the screen again into the search box...).
> > > >
> > > >Also, in the present case there was no link to the tables 
A250676 and
> > > >A250691 with almost identical definition, and they would not pop 
up
> > > >doing a search for the other sequence numbers.
> > > >
> > > >I also agree on the "significance" issue, and it is painfully to 
have
> > > >a bunch of sequence numbers in the Xrefs without knowing why 
they are
> > > >there. But with 2-3 words of explanation or just hints, this is 
a true
> > > >added value, I think.
> > > >
> > > >Maximilian
> > > >
> > > >
> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net> 
wrote:
> > > >> The row/col/diag series always link to the table, so the refs 
link
> in
> > > the table will find them.
> > > >>
> > > >> It always seemed like needless clutter to link the other way
> without a
> > > reason beyond existence.  It seems to claim significance beyond 
that.
> > > >>
> > > >> The inbound links by contrast say that there are more like 
this, in
> > > this family.
> > > >>
> > > >>
> > > >> rhhardin at mindspring.com
> > > >> rhhardin at att.net (either)
> > > >>
> > > >>
> > > >>>________________________________
> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of 
R. H.
> > > Hardin
> > > >>>
> > > >>>
> > > >>>I added your comment in A250544, and also several missing
> > > >>>cross-references to sequences which list the rows/cols.
> > > >>>It would be nice if others could edit related sequences in a 
similar
> > > manner.
> > > >>>
> > > >>>Maximilian
> > > >>>
> > > >>>
> > > >>
> > > >> _______________________________________________
> > > >>
> > > >> Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >_______________________________________________
> > > >
> > > >Seqfan Mailing list - http://list.seqfan.eu/
> > > >
> > > >
> > > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From peter.luschny at gmail.com  Wed Feb 11 21:30:20 2015
From: peter.luschny at gmail.com (Peter Luschny)
Date: Wed, 11 Feb 2015 21:30:20 +0100
Subject: [seqfan]  A marginal observation on some tables of R. H. Hardin
Message-ID: <CAMMbGZbB6H5OtU6jTzwNemCWg19bvv76aCr77TqEjMsxuQBHDw@mail.gmail.com>

The discussion went slightly off-topic, and the old habit
to change the name of a thread when the topic changes
seems to be a forgotten virtue.

But let me come back to Hardin's empirical recurrence.

I do not think that it is a coincidence that the coefficients
appear in Bala's A246117 although this is hard demonstrate
at the moment.

In the spirit of experimental math let me look also at
the recurrences a(n) and b(n) (case 2 and 3 in a more
general setup which makes Hardin's c(n) the case 4).

a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3),
b(n) = 9*b(n-1)-31*b(n-2)+51*b(n-3)-40*b(n-4)+12*b(n-5),
c(n) = 16*c(n-1)-106*c(n-2)+376*c(n-3)-769*c(n-4)+904*c(n-5)-564*c(n-6)+144*c(n-7).

So now my problem are meaningful initial terms,
a(0), a(1), a(2) and b(0), b(1), b(2), b(3), b(4).

Any suggestions for the initial terms?

Peter


From njasloane at gmail.com  Wed Feb 11 21:35:03 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 15:35:03 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
Message-ID: <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>

I cannot understand why there is ever an objection to
cross-references.

If you are using the OEIS for
what it chiefly intended for, its main purpose, which is to help
you (very often, me) understand a sequence that has come
up in your work, then any hint at all is potentially valuable.

A cross-reference is like someone whispering to you, "I don't know if it
will help, but did you look at A...... ? "

And they should all be listed in the cross-reference section,
so it is easy to find them.



Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> Just as a point of reference, a search for "A000217 -xref:A000217" gives
> 933 matches, out of 2699 that match "A000217".
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Neil Sloane <njasloane at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Feb 11, 2015 1:41 pm
> Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>
>
>  I forget.  But the main reason is for humans to be able to see at a glance
> what sequences are mentioned.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>  What part of Russ' code work improperly when a sequence is in an
>>
> entry but
>
>> not the xref field?
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
>>
> wrote:
>
>>
>> > Just to clarify one point:
>> >
>> > The rule is that if there is a line anywhere in the entry that
>> > mentions A123456, then Cf. A123456 should also appear in the
>> > cross-references section.
>> >
>> > (there are two good reasons: so Russ's code works
>> > properly, and so the user can easily see if A123456 is
>> > referred to anywhere in the entry without having to search through
>>
> every
>
>> > line)
>> >
>> > Best regards
>> > Neil
>> >
>> > Neil J. A. Sloane, President, OEIS Foundation.
>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>>
> Piscataway, NJ.
>
>> > Phone: 732 828 6098; home page: http://NeilSloane.com
>> > Email: njasloane at gmail.com
>> >
>> >
>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
>>
> wrote:
>
>> >
>> > > I agree than any specific case can benefit from two-way links,
>>
> but not
>
>> in
>> > > general.  At least it seems that way to me.
>> > >
>> > >
>> > > I don't understand the first paragraph problem you describe below.
>> > > Clicking "refs" in the header of the table gives you a nice page
>>
> with
>
>> all
>> > > the rows and columns and diagonals expanded for you, as well as
>>
> any
>
>> > foreign
>> > > sequence that happens to reference inwards.
>> > >
>> > >
>> > > rhhardin at mindspring.com
>> > > rhhardin at att.net (either)
>> > >
>> > >
>> > > >________________________________
>> > > > From: M. F. Hasler <seqfan at hasler.fr>
>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
>>
> R. H.
>
>> > > Hardin
>> > > >
>> > > >
>> > > >Ron,
>> > > >
>> > > >I am also personally against duplicating links (really never
>> > > >understood why an A-number put somewhere in comment or formula
>>
> should
>
>> > > >be repeated in Xrefs), but it is nonetheless handy to have the
>>
> links
>
>> > > >to the column sequences because else you have to do a search
>>
> with only
>
>> > > >the sequence number in order to find them via the backlink, but
>>
> often
>
>> > > >you come there following a link and not doing a search (and it is
>> > > >somehow counter-intuitive to copy-paste the number of the
>>
> sequence
>
>> > > >already displayed on the screen again into the search box...).
>> > > >
>> > > >Also, in the present case there was no link to the tables
>>
> A250676 and
>
>> > > >A250691 with almost identical definition, and they would not pop
>>
> up
>
>> > > >doing a search for the other sequence numbers.
>> > > >
>> > > >I also agree on the "significance" issue, and it is painfully to
>>
> have
>
>> > > >a bunch of sequence numbers in the Xrefs without knowing why
>>
> they are
>
>> > > >there. But with 2-3 words of explanation or just hints, this is
>>
> a true
>
>> > > >added value, I think.
>> > > >
>> > > >Maximilian
>> > > >
>> > > >
>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
>>
> wrote:
>
>> > > >> The row/col/diag series always link to the table, so the refs
>>
> link
>
>> in
>> > > the table will find them.
>> > > >>
>> > > >> It always seemed like needless clutter to link the other way
>> without a
>> > > reason beyond existence.  It seems to claim significance beyond
>>
> that.
>
>> > > >>
>> > > >> The inbound links by contrast say that there are more like
>>
> this, in
>
>> > > this family.
>> > > >>
>> > > >>
>> > > >> rhhardin at mindspring.com
>> > > >> rhhardin at att.net (either)
>> > > >>
>> > > >>
>> > > >>>________________________________
>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
>>
> R. H.
>
>> > > Hardin
>> > > >>>
>> > > >>>
>> > > >>>I added your comment in A250544, and also several missing
>> > > >>>cross-references to sequences which list the rows/cols.
>> > > >>>It would be nice if others could edit related sequences in a
>>
> similar
>
>> > > manner.
>> > > >>>
>> > > >>>Maximilian
>> > > >>>
>> > > >>>
>> > > >>
>> > > >> _______________________________________________
>> > > >>
>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
>> > > >
>> > > >
>> > > >
>> > > >
>> > > >
>> > > >_______________________________________________
>> > > >
>> > > >Seqfan Mailing list - http://list.seqfan.eu/
>> > > >
>> > > >
>> > > >
>> > >
>> > > _______________________________________________
>> > >
>> > > Seqfan Mailing list - http://list.seqfan.eu/
>> > >
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From franktaw at netscape.net  Wed Feb 11 22:33:49 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Wed, 11 Feb 2015 16:33:49 -0500
Subject: [seqfan] Cross-refs (retitled)
In-Reply-To: <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
Message-ID: <8D214598E88EBBC-B34-43019@webmail-vm109.sysops.aol.com>

I'm not disagreeing with that. I'm just pointing out how far we are 
 from doing it that way. I did at one point do some searches for "base" 
sequences that did not have the keyword, and corrected a few hundred of 
them. I'm not going to do something similar for the thousands of 
exceptions to this rule.

I guess the first step is for the editors to start uniformly enforcing 
the rule for both new and modified sequences.

Actually, I do object to cross-refs that, if all references of this 
sort were added, thousands of cross-refs would be added to a single 
sequence. Consider, for the moment, the effect of adding a cross-ref 
 from A000040 to every sequence that mentions primes. Hints are good, 
but not when you can't see the trees for the forest.

Franklin T. Adams-Watters

-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Wed, Feb 11, 2015 2:35 pm
Subject: [seqfan] Re: A marginal observation on some tables of R. H. 
Hardin


I cannot understand why there is ever an objection to
cross-references.

If you are using the OEIS for
what it chiefly intended for, its main purpose, which is to help
you (very often, me) understand a sequence that has come
up in your work, then any hint at all is potentially valuable.

A cross-reference is like someone whispering to you, "I don't know if it
will help, but did you look at A...... ? "

And they should all be listed in the cross-reference section,
so it is easy to find them.



Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters 
<franktaw at netscape.net>
wrote:

> Just as a point of reference, a search for "A000217 -xref:A000217" 
gives
> 933 matches, out of 2699 that match "A000217".
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Neil Sloane <njasloane at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Feb 11, 2015 1:41 pm
> Subject: [seqfan] Re: A marginal observation on some tables of R. H. 
Hardin
>
>
>  I forget.  But the main reason is for humans to be able to see at a 
glance
> what sequences are mentioned.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>  What part of Russ' code work improperly when a sequence is in an
>>
> entry but
>
>> not the xref field?
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
>>
> wrote:
>
>>
>> > Just to clarify one point:
>> >
>> > The rule is that if there is a line anywhere in the entry that
>> > mentions A123456, then Cf. A123456 should also appear in the
>> > cross-references section.
>> >
>> > (there are two good reasons: so Russ's code works
>> > properly, and so the user can easily see if A123456 is
>> > referred to anywhere in the entry without having to search through
>>
> every
>
>> > line)
>> >
>> > Best regards
>> > Neil
>> >
>> > Neil J. A. Sloane, President, OEIS Foundation.
>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>>
> Piscataway, NJ.
>
>> > Phone: 732 828 6098; home page: http://NeilSloane.com
>> > Email: njasloane at gmail.com
>> >
>> >
>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
>>
> wrote:
>
>> >
>> > > I agree than any specific case can benefit from two-way links,
>>
> but not
>
>> in
>> > > general.  At least it seems that way to me.
>> > >
>> > >
>> > > I don't understand the first paragraph problem you describe 
below.
>> > > Clicking "refs" in the header of the table gives you a nice page
>>
> with
>
>> all
>> > > the rows and columns and diagonals expanded for you, as well as
>>
> any
>
>> > foreign
>> > > sequence that happens to reference inwards.
>> > >
>> > >
>> > > rhhardin at mindspring.com
>> > > rhhardin at att.net (either)
>> > >
>> > >
>> > > >________________________________
>> > > > From: M. F. Hasler <seqfan at hasler.fr>
>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
>>
> R. H.
>
>> > > Hardin
>> > > >
>> > > >
>> > > >Ron,
>> > > >
>> > > >I am also personally against duplicating links (really never
>> > > >understood why an A-number put somewhere in comment or formula
>>
> should
>
>> > > >be repeated in Xrefs), but it is nonetheless handy to have the
>>
> links
>
>> > > >to the column sequences because else you have to do a search
>>
> with only
>
>> > > >the sequence number in order to find them via the backlink, but
>>
> often
>
>> > > >you come there following a link and not doing a search (and it 
is
>> > > >somehow counter-intuitive to copy-paste the number of the
>>
> sequence
>
>> > > >already displayed on the screen again into the search box...).
>> > > >
>> > > >Also, in the present case there was no link to the tables
>>
> A250676 and
>
>> > > >A250691 with almost identical definition, and they would not pop
>>
> up
>
>> > > >doing a search for the other sequence numbers.
>> > > >
>> > > >I also agree on the "significance" issue, and it is painfully to
>>
> have
>
>> > > >a bunch of sequence numbers in the Xrefs without knowing why
>>
> they are
>
>> > > >there. But with 2-3 words of explanation or just hints, this is
>>
> a true
>
>> > > >added value, I think.
>> > > >
>> > > >Maximilian
>> > > >
>> > > >
>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
>>
> wrote:
>
>> > > >> The row/col/diag series always link to the table, so the refs
>>
> link
>
>> in
>> > > the table will find them.
>> > > >>
>> > > >> It always seemed like needless clutter to link the other way
>> without a
>> > > reason beyond existence.  It seems to claim significance beyond
>>
> that.
>
>> > > >>
>> > > >> The inbound links by contrast say that there are more like
>>
> this, in
>
>> > > this family.
>> > > >>
>> > > >>
>> > > >> rhhardin at mindspring.com
>> > > >> rhhardin at att.net (either)
>> > > >>
>> > > >>
>> > > >>>________________________________
>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
>>
> R. H.
>
>> > > Hardin
>> > > >>>
>> > > >>>
>> > > >>>I added your comment in A250544, and also several missing
>> > > >>>cross-references to sequences which list the rows/cols.
>> > > >>>It would be nice if others could edit related sequences in a
>>
> similar
>
>> > > manner.
>> > > >>>
>> > > >>>Maximilian
>> > > >>>
>> > > >>>
>> > > >>
>> > > >> _______________________________________________
>> > > >>
>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
>> > > >
>> > > >
>> > > >
>> > > >
>> > > >
>> > > >_______________________________________________
>> > > >
>> > > >Seqfan Mailing list - http://list.seqfan.eu/
>> > > >
>> > > >
>> > > >
>> > >
>> > > _______________________________________________
>> > >
>> > > Seqfan Mailing list - http://list.seqfan.eu/
>> > >
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From njasloane at gmail.com  Wed Feb 11 22:54:50 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 16:54:50 -0500
Subject: [seqfan] Re: Cross-refs (retitled)
In-Reply-To: <8D214598E88EBBC-B34-43019@webmail-vm109.sysops.aol.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
 <8D214598E88EBBC-B34-43019@webmail-vm109.sysops.aol.com>
Message-ID: <CAAOnSgQwmzTMTk9WKQc0USfOFuMR6Z8Jy3G98yJQ=P7=Vb6+pg@mail.gmail.com>

I certainly was not suggesting that if A references B then B should
reference A.  That has never been a rule.

(There are remarks about this in one of the ancient
"format of entries" files.)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 4:33 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> I'm not disagreeing with that. I'm just pointing out how far we are from
> doing it that way. I did at one point do some searches for "base" sequences
> that did not have the keyword, and corrected a few hundred of them. I'm not
> going to do something similar for the thousands of exceptions to this rule.
>
> I guess the first step is for the editors to start uniformly enforcing the
> rule for both new and modified sequences.
>
> Actually, I do object to cross-refs that, if all references of this sort
> were added, thousands of cross-refs would be added to a single sequence.
> Consider, for the moment, the effect of adding a cross-ref from A000040 to
> every sequence that mentions primes. Hints are good, but not when you can't
> see the trees for the forest.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Neil Sloane <njasloane at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Feb 11, 2015 2:35 pm
> Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>
>
> I cannot understand why there is ever an objection to
> cross-references.
>
> If you are using the OEIS for
> what it chiefly intended for, its main purpose, which is to help
> you (very often, me) understand a sequence that has come
> up in your work, then any hint at all is potentially valuable.
>
> A cross-reference is like someone whispering to you, "I don't know if it
> will help, but did you look at A...... ? "
>
> And they should all be listed in the cross-reference section,
> so it is easy to find them.
>
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters <
> franktaw at netscape.net>
> wrote:
>
>  Just as a point of reference, a search for "A000217 -xref:A000217"
>>
> gives
>
>> 933 matches, out of 2699 that match "A000217".
>>
>> Franklin T. Adams-Watters
>>
>> -----Original Message-----
>> From: Neil Sloane <njasloane at gmail.com>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Wed, Feb 11, 2015 1:41 pm
>> Subject: [seqfan] Re: A marginal observation on some tables of R. H.
>>
> Hardin
>
>>
>>
>>  I forget.  But the main reason is for humans to be able to see at a
>>
> glance
>
>> what sequences are mentioned.
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
>>
> NJ.
>
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
>> charles.greathouse at case.edu> wrote:
>>
>>  What part of Russ' code work improperly when a sequence is in an
>>
>>>
>>>  entry but
>>
>>  not the xref field?
>>>
>>> Charles Greathouse
>>> Analyst/Programmer
>>> Case Western Reserve University
>>>
>>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
>>>
>>>  wrote:
>>
>>
>>> > Just to clarify one point:
>>> >
>>> > The rule is that if there is a line anywhere in the entry that
>>> > mentions A123456, then Cf. A123456 should also appear in the
>>> > cross-references section.
>>> >
>>> > (there are two good reasons: so Russ's code works
>>> > properly, and so the user can easily see if A123456 is
>>> > referred to anywhere in the entry without having to search through
>>>
>>>  every
>>
>>  > line)
>>> >
>>> > Best regards
>>> > Neil
>>> >
>>> > Neil J. A. Sloane, President, OEIS Foundation.
>>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>>>
>>>  Piscataway, NJ.
>>
>>  > Phone: 732 828 6098; home page: http://NeilSloane.com
>>> > Email: njasloane at gmail.com
>>> >
>>> >
>>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
>>>
>>>  wrote:
>>
>>  >
>>> > > I agree than any specific case can benefit from two-way links,
>>>
>>>  but not
>>
>>  in
>>> > > general.  At least it seems that way to me.
>>> > >
>>> > >
>>> > > I don't understand the first paragraph problem you describe
>>>
>> below.
>
>> > > Clicking "refs" in the header of the table gives you a nice page
>>>
>>>  with
>>
>>  all
>>> > > the rows and columns and diagonals expanded for you, as well as
>>>
>>>  any
>>
>>  > foreign
>>> > > sequence that happens to reference inwards.
>>> > >
>>> > >
>>> > > rhhardin at mindspring.com
>>> > > rhhardin at att.net (either)
>>> > >
>>> > >
>>> > > >________________________________
>>> > > > From: M. F. Hasler <seqfan at hasler.fr>
>>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
>>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
>>>
>>>  R. H.
>>
>>  > > Hardin
>>> > > >
>>> > > >
>>> > > >Ron,
>>> > > >
>>> > > >I am also personally against duplicating links (really never
>>> > > >understood why an A-number put somewhere in comment or formula
>>>
>>>  should
>>
>>  > > >be repeated in Xrefs), but it is nonetheless handy to have the
>>>
>>>  links
>>
>>  > > >to the column sequences because else you have to do a search
>>>
>>>  with only
>>
>>  > > >the sequence number in order to find them via the backlink, but
>>>
>>>  often
>>
>>  > > >you come there following a link and not doing a search (and it
>>>
>> is
>
>> > > >somehow counter-intuitive to copy-paste the number of the
>>>
>>>  sequence
>>
>>  > > >already displayed on the screen again into the search box...).
>>> > > >
>>> > > >Also, in the present case there was no link to the tables
>>>
>>>  A250676 and
>>
>>  > > >A250691 with almost identical definition, and they would not pop
>>>
>>>  up
>>
>>  > > >doing a search for the other sequence numbers.
>>> > > >
>>> > > >I also agree on the "significance" issue, and it is painfully to
>>>
>>>  have
>>
>>  > > >a bunch of sequence numbers in the Xrefs without knowing why
>>>
>>>  they are
>>
>>  > > >there. But with 2-3 words of explanation or just hints, this is
>>>
>>>  a true
>>
>>  > > >added value, I think.
>>> > > >
>>> > > >Maximilian
>>> > > >
>>> > > >
>>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
>>>
>>>  wrote:
>>
>>  > > >> The row/col/diag series always link to the table, so the refs
>>>
>>>  link
>>
>>  in
>>> > > the table will find them.
>>> > > >>
>>> > > >> It always seemed like needless clutter to link the other way
>>> without a
>>> > > reason beyond existence.  It seems to claim significance beyond
>>>
>>>  that.
>>
>>  > > >>
>>> > > >> The inbound links by contrast say that there are more like
>>>
>>>  this, in
>>
>>  > > this family.
>>> > > >>
>>> > > >>
>>> > > >> rhhardin at mindspring.com
>>> > > >> rhhardin at att.net (either)
>>> > > >>
>>> > > >>
>>> > > >>>________________________________
>>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
>>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
>>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
>>>
>>>  R. H.
>>
>>  > > Hardin
>>> > > >>>
>>> > > >>>
>>> > > >>>I added your comment in A250544, and also several missing
>>> > > >>>cross-references to sequences which list the rows/cols.
>>> > > >>>It would be nice if others could edit related sequences in a
>>>
>>>  similar
>>
>>  > > manner.
>>> > > >>>
>>> > > >>>Maximilian
>>> > > >>>
>>> > > >>>
>>> > > >>
>>> > > >> _______________________________________________
>>> > > >>
>>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
>>> > > >
>>> > > >
>>> > > >
>>> > > >
>>> > > >
>>> > > >_______________________________________________
>>> > > >
>>> > > >Seqfan Mailing list - http://list.seqfan.eu/
>>> > > >
>>> > > >
>>> > > >
>>> > >
>>> > > _______________________________________________
>>> > >
>>> > > Seqfan Mailing list - http://list.seqfan.eu/
>>> > >
>>> >
>>> > _______________________________________________
>>> >
>>> > Seqfan Mailing list - http://list.seqfan.eu/
>>> >
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>>>  _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From rhhardin at att.net  Wed Feb 11 23:05:57 2015
From: rhhardin at att.net (Ron Hardin)
Date: Wed, 11 Feb 2015 14:05:57 -0800
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
Message-ID: <1423692357.25896.YahooMailNeo@web185002.mail.gq1.yahoo.com>

It's easy to add the %Y lines (done!) to the generating programs but it changes how you look at the line if it's an index of mentions above rather than something you might want to look at as decided by a human.  Either way is okay.  It just changes the use.

The count-against is that you lose the human editor, and so may skip them all because so many are useless.

 
rhhardin at mindspring.com
rhhardin at att.net (either)


>________________________________
> From: Neil Sloane <njasloane at gmail.com>
>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
>Sent: Wednesday, February 11, 2015 3:35 PM
>Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
> 
>
>I cannot understand why there is ever an objection to
>cross-references.
>
>If you are using the OEIS for
>what it chiefly intended for, its main purpose, which is to help
>you (very often, me) understand a sequence that has come
>up in your work, then any hint at all is potentially valuable.
>
>A cross-reference is like someone whispering to you, "I don't know if it
>will help, but did you look at A...... ? "
>
>And they should all be listed in the cross-reference section,
>so it is easy to find them.
>
>
>
>Best regards
>Neil
>
>Neil J. A. Sloane, President, OEIS Foundation.
>11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>Phone: 732 828 6098; home page: http://NeilSloane.com
>Email: njasloane at gmail.com
>
>
>On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters <franktaw at netscape.net>
>wrote:
>
>> Just as a point of reference, a search for "A000217 -xref:A000217" gives
>> 933 matches, out of 2699 that match "A000217".
>>
>> Franklin T. Adams-Watters
>>
>> -----Original Message-----
>> From: Neil Sloane <njasloane at gmail.com>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Wed, Feb 11, 2015 1:41 pm
>> Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
>>
>>
>>  I forget.  But the main reason is for humans to be able to see at a glance
>> what sequences are mentioned.
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
>> charles.greathouse at case.edu> wrote:
>>
>>  What part of Russ' code work improperly when a sequence is in an
>>>
>> entry but
>>
>>> not the xref field?
>>>
>>> Charles Greathouse
>>> Analyst/Programmer
>>> Case Western Reserve University
>>>
>>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
>>>
>> wrote:
>>
>>>
>>> > Just to clarify one point:
>>> >
>>> > The rule is that if there is a line anywhere in the entry that
>>> > mentions A123456, then Cf. A123456 should also appear in the
>>> > cross-references section.
>>> >
>>> > (there are two good reasons: so Russ's code works
>>> > properly, and so the user can easily see if A123456 is
>>> > referred to anywhere in the entry without having to search through
>>>
>> every
>>
>>> > line)
>>> >
>>> > Best regards
>>> > Neil
>>> >
>>> > Neil J. A. Sloane, President, OEIS Foundation.
>>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>>> > Also Visiting Scientist, Math. Dept., Rutgers University,
>>>
>> Piscataway, NJ.
>>
>>> > Phone: 732 828 6098; home page: http://NeilSloane.com
>>> > Email: njasloane at gmail.com
>>> >
>>> >
>>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
>>>
>> wrote:
>>
>>> >
>>> > > I agree than any specific case can benefit from two-way links,
>>>
>> but not
>>
>>> in
>>> > > general.  At least it seems that way to me.
>>> > >
>>> > >
>>> > > I don't understand the first paragraph problem you describe below.
>>> > > Clicking "refs" in the header of the table gives you a nice page
>>>
>> with
>>
>>> all
>>> > > the rows and columns and diagonals expanded for you, as well as
>>>
>> any
>>
>>> > foreign
>>> > > sequence that happens to reference inwards.
>>> > >
>>> > >
>>> > > rhhardin at mindspring.com
>>> > > rhhardin at att.net (either)
>>> > >
>>> > >
>>> > > >________________________________
>>> > > > From: M. F. Hasler <seqfan at hasler.fr>
>>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
>>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
>>>
>> R. H.
>>
>>> > > Hardin
>>> > > >
>>> > > >
>>> > > >Ron,
>>> > > >
>>> > > >I am also personally against duplicating links (really never
>>> > > >understood why an A-number put somewhere in comment or formula
>>>
>> should
>>
>>> > > >be repeated in Xrefs), but it is nonetheless handy to have the
>>>
>> links
>>
>>> > > >to the column sequences because else you have to do a search
>>>
>> with only
>>
>>> > > >the sequence number in order to find them via the backlink, but
>>>
>> often
>>
>>> > > >you come there following a link and not doing a search (and it is
>>> > > >somehow counter-intuitive to copy-paste the number of the
>>>
>> sequence
>>
>>> > > >already displayed on the screen again into the search box...).
>>> > > >
>>> > > >Also, in the present case there was no link to the tables
>>>
>> A250676 and
>>
>>> > > >A250691 with almost identical definition, and they would not pop
>>>
>> up
>>
>>> > > >doing a search for the other sequence numbers.
>>> > > >
>>> > > >I also agree on the "significance" issue, and it is painfully to
>>>
>> have
>>
>>> > > >a bunch of sequence numbers in the Xrefs without knowing why
>>>
>> they are
>>
>>> > > >there. But with 2-3 words of explanation or just hints, this is
>>>
>> a true
>>
>>> > > >added value, I think.
>>> > > >
>>> > > >Maximilian
>>> > > >
>>> > > >
>>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
>>>
>> wrote:
>>
>>> > > >> The row/col/diag series always link to the table, so the refs
>>>
>> link
>>
>>> in
>>> > > the table will find them.
>>> > > >>
>>> > > >> It always seemed like needless clutter to link the other way
>>> without a
>>> > > reason beyond existence.  It seems to claim significance beyond
>>>
>> that.
>>
>>> > > >>
>>> > > >> The inbound links by contrast say that there are more like
>>>
>> this, in
>>
>>> > > this family.
>>> > > >>
>>> > > >>
>>> > > >> rhhardin at mindspring.com
>>> > > >> rhhardin at att.net (either)
>>> > > >>
>>> > > >>
>>> > > >>>________________________________
>>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
>>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
>>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
>>>
>> R. H.
>>
>>> > > Hardin
>>> > > >>>
>>> > > >>>
>>> > > >>>I added your comment in A250544, and also several missing
>>> > > >>>cross-references to sequences which list the rows/cols.
>>> > > >>>It would be nice if others could edit related sequences in a
>>>
>> similar
>>
>>> > > manner.
>>> > > >>>
>>> > > >>>Maximilian
>>> > > >>>
>>> > > >>>
>>> > > >>
>>> > > >> _______________________________________________
>>> > > >>
>>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>>> > > >
>>> > > >
>>> > > >
>>> > > >
>>> > > >
>>> > > >_______________________________________________
>>> > > >
>>> > > >Seqfan Mailing list - http://list.seqfan.eu/
>>> > > >
>>> > > >
>>> > > >
>>> > >
>>> > > _______________________________________________
>>> > >
>>> > > Seqfan Mailing list - http://list.seqfan.eu/
>>> > >
>>> >
>>> > _______________________________________________
>>> >
>>> > Seqfan Mailing list - http://list.seqfan.eu/
>>> >
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>
>


From njasloane at gmail.com  Wed Feb 11 23:55:25 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Wed, 11 Feb 2015 17:55:25 -0500
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <1423692357.25896.YahooMailNeo@web185002.mail.gq1.yahoo.com>
References: <CAMMbGZa3-Ht2HGmnbw8EJhxGuG66QdUG9rcwFK32BFiwSbBRyg@mail.gmail.com>
 <CABxCbJ225ibem=Wrkeu8NBwPnsfLGxSvYgVj12PuW2dU+g-GiQ@mail.gmail.com>
 <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
 <1423692357.25896.YahooMailNeo@web185002.mail.gq1.yahoo.com>
Message-ID: <CAAOnSgSSGykvFU3HHuuSDG0Ph6Scr6EA1nu_E54-THuT6QUEbQ@mail.gmail.com>

Good point, about discouraging human readers.

How about something like this? The machine-generated
cross-references could say:

Cf. (generated automatically): A234111, A234112, ...

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Wed, Feb 11, 2015 at 5:05 PM, Ron Hardin <rhhardin at att.net> wrote:

> It's easy to add the %Y lines (done!) to the generating programs but it
> changes how you look at the line if it's an index of mentions above rather
> than something you might want to look at as decided by a human.  Either way
> is okay.  It just changes the use.
>
> The count-against is that you lose the human editor, and so may skip them
> all because so many are useless.
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
>
> >________________________________
> > From: Neil Sloane <njasloane at gmail.com>
> >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >Sent: Wednesday, February 11, 2015 3:35 PM
> >Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> Hardin
> >
> >
> >I cannot understand why there is ever an objection to
> >cross-references.
> >
> >If you are using the OEIS for
> >what it chiefly intended for, its main purpose, which is to help
> >you (very often, me) understand a sequence that has come
> >up in your work, then any hint at all is potentially valuable.
> >
> >A cross-reference is like someone whispering to you, "I don't know if it
> >will help, but did you look at A...... ? "
> >
> >And they should all be listed in the cross-reference section,
> >so it is easy to find them.
> >
> >
> >
> >Best regards
> >Neil
> >
> >Neil J. A. Sloane, President, OEIS Foundation.
> >11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> >Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> >Phone: 732 828 6098; home page: http://NeilSloane.com
> >Email: njasloane at gmail.com
> >
> >
> >On Wed, Feb 11, 2015 at 2:56 PM, Frank Adams-Watters <
> franktaw at netscape.net>
> >wrote:
> >
> >> Just as a point of reference, a search for "A000217 -xref:A000217" gives
> >> 933 matches, out of 2699 that match "A000217".
> >>
> >> Franklin T. Adams-Watters
> >>
> >> -----Original Message-----
> >> From: Neil Sloane <njasloane at gmail.com>
> >> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >> Sent: Wed, Feb 11, 2015 1:41 pm
> >> Subject: [seqfan] Re: A marginal observation on some tables of R. H.
> Hardin
> >>
> >>
> >>  I forget.  But the main reason is for humans to be able to see at a
> glance
> >> what sequences are mentioned.
> >>
> >> Best regards
> >> Neil
> >>
> >> Neil J. A. Sloane, President, OEIS Foundation.
> >> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> >> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
> NJ.
> >> Phone: 732 828 6098; home page: http://NeilSloane.com
> >> Email: njasloane at gmail.com
> >>
> >>
> >> On Wed, Feb 11, 2015 at 2:15 PM, Charles Greathouse <
> >> charles.greathouse at case.edu> wrote:
> >>
> >>  What part of Russ' code work improperly when a sequence is in an
> >>>
> >> entry but
> >>
> >>> not the xref field?
> >>>
> >>> Charles Greathouse
> >>> Analyst/Programmer
> >>> Case Western Reserve University
> >>>
> >>> On Wed, Feb 11, 2015 at 11:23 AM, Neil Sloane <njasloane at gmail.com>
> >>>
> >> wrote:
> >>
> >>>
> >>> > Just to clarify one point:
> >>> >
> >>> > The rule is that if there is a line anywhere in the entry that
> >>> > mentions A123456, then Cf. A123456 should also appear in the
> >>> > cross-references section.
> >>> >
> >>> > (there are two good reasons: so Russ's code works
> >>> > properly, and so the user can easily see if A123456 is
> >>> > referred to anywhere in the entry without having to search through
> >>>
> >> every
> >>
> >>> > line)
> >>> >
> >>> > Best regards
> >>> > Neil
> >>> >
> >>> > Neil J. A. Sloane, President, OEIS Foundation.
> >>> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> >>> > Also Visiting Scientist, Math. Dept., Rutgers University,
> >>>
> >> Piscataway, NJ.
> >>
> >>> > Phone: 732 828 6098; home page: http://NeilSloane.com
> >>> > Email: njasloane at gmail.com
> >>> >
> >>> >
> >>> > On Wed, Feb 11, 2015 at 7:34 AM, Ron Hardin <rhhardin at att.net>
> >>>
> >> wrote:
> >>
> >>> >
> >>> > > I agree than any specific case can benefit from two-way links,
> >>>
> >> but not
> >>
> >>> in
> >>> > > general.  At least it seems that way to me.
> >>> > >
> >>> > >
> >>> > > I don't understand the first paragraph problem you describe below.
> >>> > > Clicking "refs" in the header of the table gives you a nice page
> >>>
> >> with
> >>
> >>> all
> >>> > > the rows and columns and diagonals expanded for you, as well as
> >>>
> >> any
> >>
> >>> > foreign
> >>> > > sequence that happens to reference inwards.
> >>> > >
> >>> > >
> >>> > > rhhardin at mindspring.com
> >>> > > rhhardin at att.net (either)
> >>> > >
> >>> > >
> >>> > > >________________________________
> >>> > > > From: M. F. Hasler <seqfan at hasler.fr>
> >>> > > >To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >>> > > >Sent: Wednesday, February 11, 2015 7:23 AM
> >>> > > >Subject: [seqfan] Re: A marginal observation on some tables of
> >>>
> >> R. H.
> >>
> >>> > > Hardin
> >>> > > >
> >>> > > >
> >>> > > >Ron,
> >>> > > >
> >>> > > >I am also personally against duplicating links (really never
> >>> > > >understood why an A-number put somewhere in comment or formula
> >>>
> >> should
> >>
> >>> > > >be repeated in Xrefs), but it is nonetheless handy to have the
> >>>
> >> links
> >>
> >>> > > >to the column sequences because else you have to do a search
> >>>
> >> with only
> >>
> >>> > > >the sequence number in order to find them via the backlink, but
> >>>
> >> often
> >>
> >>> > > >you come there following a link and not doing a search (and it is
> >>> > > >somehow counter-intuitive to copy-paste the number of the
> >>>
> >> sequence
> >>
> >>> > > >already displayed on the screen again into the search box...).
> >>> > > >
> >>> > > >Also, in the present case there was no link to the tables
> >>>
> >> A250676 and
> >>
> >>> > > >A250691 with almost identical definition, and they would not pop
> >>>
> >> up
> >>
> >>> > > >doing a search for the other sequence numbers.
> >>> > > >
> >>> > > >I also agree on the "significance" issue, and it is painfully to
> >>>
> >> have
> >>
> >>> > > >a bunch of sequence numbers in the Xrefs without knowing why
> >>>
> >> they are
> >>
> >>> > > >there. But with 2-3 words of explanation or just hints, this is
> >>>
> >> a true
> >>
> >>> > > >added value, I think.
> >>> > > >
> >>> > > >Maximilian
> >>> > > >
> >>> > > >
> >>> > > >On Wed, Feb 11, 2015 at 8:05 AM, Ron Hardin <rhhardin at att.net>
> >>>
> >> wrote:
> >>
> >>> > > >> The row/col/diag series always link to the table, so the refs
> >>>
> >> link
> >>
> >>> in
> >>> > > the table will find them.
> >>> > > >>
> >>> > > >> It always seemed like needless clutter to link the other way
> >>> without a
> >>> > > reason beyond existence.  It seems to claim significance beyond
> >>>
> >> that.
> >>
> >>> > > >>
> >>> > > >> The inbound links by contrast say that there are more like
> >>>
> >> this, in
> >>
> >>> > > this family.
> >>> > > >>
> >>> > > >>
> >>> > > >> rhhardin at mindspring.com
> >>> > > >> rhhardin at att.net (either)
> >>> > > >>
> >>> > > >>
> >>> > > >>>________________________________
> >>> > > >>> From: M. F. Hasler <seqfan at hasler.fr>
> >>> > > >>>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >>> > > >>>Sent: Wednesday, February 11, 2015 6:48 AM
> >>> > > >>>Subject: [seqfan] Re: A marginal observation on some tables of
> >>>
> >> R. H.
> >>
> >>> > > Hardin
> >>> > > >>>
> >>> > > >>>
> >>> > > >>>I added your comment in A250544, and also several missing
> >>> > > >>>cross-references to sequences which list the rows/cols.
> >>> > > >>>It would be nice if others could edit related sequences in a
> >>>
> >> similar
> >>
> >>> > > manner.
> >>> > > >>>
> >>> > > >>>Maximilian
> >>> > > >>>
> >>> > > >>>
> >>> > > >>
> >>> > > >> _______________________________________________
> >>> > > >>
> >>> > > >> Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> >
> >>> > > >
> >>> > > >
> >>> > > >
> >>> > > >
> >>> > > >
> >>> > > >_______________________________________________
> >>> > > >
> >>> > > >Seqfan Mailing list - http://list.seqfan.eu/
> >>> > > >
> >>> > > >
> >>> > > >
> >>> > >
> >>> > > _______________________________________________
> >>> > >
> >>> > > Seqfan Mailing list - http://list.seqfan.eu/
> >>> > >
> >>> >
> >>> > _______________________________________________
> >>> >
> >>> > Seqfan Mailing list - http://list.seqfan.eu/
> >>> >
> >>>
> >>> _______________________________________________
> >>>
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
> >>>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >_______________________________________________
> >
> >Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From michel.marcus at free.fr  Wed Feb 11 21:15:17 2015
From: michel.marcus at free.fr (michel.marcus at free.fr)
Date: Wed, 11 Feb 2015 21:15:17 +0100 (CET)
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <1588911053.534795074.1423685610707.JavaMail.root@spooler7-g27.priv.proxad.net>
Message-ID: <115735703.534802904.1423685717411.JavaMail.root@spooler7-g27.priv.proxad.net>

I guess that's why the "refs" link in A000217 is: A000217 -id:A000217 . 


Michel Marcus 


From zbi74583.boat at orange.zero.jp  Mon Feb  9 07:43:48 2015
From: zbi74583.boat at orange.zero.jp (zbi74583.boat at orange.zero.jp)
Date: Mon, 9 Feb 2015 15:43:48 +0900 (JST)
Subject: [seqfan] Generalized Amicable Number
Message-ID: <65391.114.49.34.179.1423464228.squirrel@webmail.zero.jp>

    Hi,Seqfans
    I genaralized Amicable Number as follows

    (-1)Sigma(x)=(-1)Sigma(y)=8/5*(x*y)^(1/2)

    The definition of (-1)Sigma(x) is here A049060

    I computed it by hand

    x = 5^2*11*29*2^2*3^2
    y = 5^2*11*29*7^2

    x = y
      = 2^2*3^3*5^2*7*19*29

    x = 3^3*7*19*29*2^4
    y = 3^3*7*19*29*5^2

    Could anyon confirm them and compute
    more term?



    Yasutoshi




From jfb at brennen.net  Thu Feb 12 18:05:53 2015
From: jfb at brennen.net (Jack Brennen)
Date: Thu, 12 Feb 2015 09:05:53 -0800
Subject: [seqfan] Re: Generalized Amicable Number
In-Reply-To: <65391.114.49.34.179.1423464228.squirrel@webmail.zero.jp>
References: <65391.114.49.34.179.1423464228.squirrel@webmail.zero.jp>
Message-ID: <54DCDD71.6050003@brennen.net>

For your first pair, it seems that they satisfy the equation:

    (-1)Sigma(x)=(-1)Sigma(y)=4/3*(x*y)^(1/2)

I can confirm that the other two you provided are correct.

Is it possible that the ratio of 8/5 doesn't need to be
fixed, but instead of the form 2-2/p ?  Given the significance
of the "-2" in the computation of (-1)Sigma(x), I could imagine
how that might make sense.

Pairs that I found that satisfy the equation at the given 8/5
ratio include:

x = y = 2^3*3^3*5*13*19

x = 3^3*7*19*29*2^4
y = 3^3*7*19*29*5^2           {Your 3rd pair}

x = y = 2^4*3^3*5*7*19*29
x = y = 2^2*3^3*5^2*7*19*29   {Your 2nd pair}
x = y = 2^2*3^3*5^3*7*11*19
x = y = 2^6*3*5^5*61
x = y = 2^3*3^2*5^2*7*11*13*29


On 2/8/2015 10:43 PM, zbi74583.boat at orange.zero.jp wrote:
>      Hi,Seqfans
>      I genaralized Amicable Number as follows
>
>      (-1)Sigma(x)=(-1)Sigma(y)=8/5*(x*y)^(1/2)
>
>      The definition of (-1)Sigma(x) is here A049060
>
>      I computed it by hand
>
>      x = 5^2*11*29*2^2*3^2
>      y = 5^2*11*29*7^2
>
>      x = y
>        = 2^2*3^3*5^2*7*19*29
>
>      x = 3^3*7*19*29*2^4
>      y = 3^3*7*19*29*5^2
>
>      Could anyon confirm them and compute
>      more term?
>
>
>
>      Yasutoshi
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>



From hpd at hpdale.org  Sat Feb 14 01:59:34 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 14 Feb 2015 00:59:34 +0000
Subject: [seqfan] A133579
Message-ID: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>

	I cannot figure out how to generate the terms of the above sequence from its definition.
	Best,
	Harvey


From franktaw at netscape.net  Sat Feb 14 02:33:18 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Fri, 13 Feb 2015 20:33:18 -0500
Subject: [seqfan] Re: A133579
In-Reply-To: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
Message-ID: <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>

The definition is clearly wrong, since gcd(n,a(n-1)) always divides 
a(n-1).

A133580 seems to be related, and may provide a clue. (BTW, the offset 
for A133580 is wrong; from the definition it should be 0.)

Franklin T. Adams-Watters

-----Original Message-----
From: Harvey P. Dale <hpd at hpdale.org>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Feb 13, 2015 6:59 pm
Subject: [seqfan] A133579


	I cannot figure out how to generate the terms of the above sequence 
from its
definition.
	Best,
	Harvey

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From njasloane at gmail.com  Sat Feb 14 03:13:06 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Fri, 13 Feb 2015 21:13:06 -0500
Subject: [seqfan] Re: A133579
In-Reply-To: <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
Message-ID: <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>

First, about A133580: the definition was correct, and the terms were
correct, but the offset should have been 0.  I changed the offset and added
some example lines to clarify the situation.

The b-file is now wrong, unfortunately (Harvey, could you correct it?), and
probably the programs also need correcting.

Following Franklin's hint, this suggests that the correct
definition of A133579 should be:

a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime,
otherwise a(n) = a(n-1)/gcd(a(n-1),n).

This almost matches the terms, but there is a mistake at
a(6), I believe, - as Harvey noticed - so it
needs to be recomputed. (a(6) should be 1 not 9). The offset is also wrong,
it should be 0, and I will fix that.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> The definition is clearly wrong, since gcd(n,a(n-1)) always divides a(n-1).
>
> A133580 seems to be related, and may provide a clue. (BTW, the offset for
> A133580 is wrong; from the definition it should be 0.)
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Harvey P. Dale <hpd at hpdale.org>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Feb 13, 2015 6:59 pm
> Subject: [seqfan] A133579
>
>
>         I cannot figure out how to generate the terms of the above
> sequence from its
> definition.
>         Best,
>         Harvey
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Sat Feb 14 03:21:53 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Fri, 13 Feb 2015 21:21:53 -0500
Subject: [seqfan] Re: A133579
In-Reply-To: <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
 <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
Message-ID: <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>

A133058 needed  a similar correction (and lacks a b-file - Harvey?)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 13, 2015 at 9:13 PM, Neil Sloane <njasloane at gmail.com> wrote:

> First, about A133580: the definition was correct, and the terms were
> correct, but the offset should have been 0.  I changed the offset and added
> some example lines to clarify the situation.
>
> The b-file is now wrong, unfortunately (Harvey, could you correct it?),
> and probably the programs also need correcting.
>
> Following Franklin's hint, this suggests that the correct
> definition of A133579 should be:
>
> a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime,
> otherwise a(n) = a(n-1)/gcd(a(n-1),n).
>
> This almost matches the terms, but there is a mistake at
> a(6), I believe, - as Harvey noticed - so it
> needs to be recomputed. (a(6) should be 1 not 9). The offset is also wrong,
> it should be 0, and I will fix that.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters <
> franktaw at netscape.net> wrote:
>
>> The definition is clearly wrong, since gcd(n,a(n-1)) always divides
>> a(n-1).
>>
>> A133580 seems to be related, and may provide a clue. (BTW, the offset for
>> A133580 is wrong; from the definition it should be 0.)
>>
>> Franklin T. Adams-Watters
>>
>>
>> -----Original Message-----
>> From: Harvey P. Dale <hpd at hpdale.org>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Fri, Feb 13, 2015 6:59 pm
>> Subject: [seqfan] A133579
>>
>>
>>         I cannot figure out how to generate the terms of the above
>> sequence from its
>> definition.
>>         Best,
>>         Harvey
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>


From hpd at hpdale.org  Sat Feb 14 17:33:23 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 14 Feb 2015 16:33:23 +0000
Subject: [seqfan] Re: A133579
In-Reply-To: <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
 <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
 <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>
Message-ID: <CY1PR0401MB106882AC1B98B9DFA0598C2FC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>

	I checked the Mma programs for A133580 and they are still okay even after the offset was changed.  I recomputed the b-file to reflect the changed offset and the new b-file has now been uploaded.
	I cannot generate the terms of A133579 even using Neil's revised definition so I suspect the revised definition is still not correct.
	Best,
	Harvey

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil Sloane
Sent: Friday, February 13, 2015 9:22 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: A133579

A133058 needed  a similar correction (and lacks a b-file - Harvey?)

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 13, 2015 at 9:13 PM, Neil Sloane <njasloane at gmail.com> wrote:

> First, about A133580: the definition was correct, and the terms were 
> correct, but the offset should have been 0.  I changed the offset and 
> added some example lines to clarify the situation.
>
> The b-file is now wrong, unfortunately (Harvey, could you correct 
> it?), and probably the programs also need correcting.
>
> Following Franklin's hint, this suggests that the correct definition 
> of A133579 should be:
>
> a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime, 
> otherwise a(n) = a(n-1)/gcd(a(n-1),n).
>
> This almost matches the terms, but there is a mistake at a(6), I 
> believe, - as Harvey noticed - so it needs to be recomputed. (a(6) 
> should be 1 not 9). The offset is also wrong, it should be 0, and I 
> will fix that.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters < 
> franktaw at netscape.net> wrote:
>
>> The definition is clearly wrong, since gcd(n,a(n-1)) always divides 
>> a(n-1).
>>
>> A133580 seems to be related, and may provide a clue. (BTW, the offset 
>> for
>> A133580 is wrong; from the definition it should be 0.)
>>
>> Franklin T. Adams-Watters
>>
>>
>> -----Original Message-----
>> From: Harvey P. Dale <hpd at hpdale.org>
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> Sent: Fri, Feb 13, 2015 6:59 pm
>> Subject: [seqfan] A133579
>>
>>
>>         I cannot figure out how to generate the terms of the above 
>> sequence from its definition.
>>         Best,
>>         Harvey
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/

From hpd at hpdale.org  Sat Feb 14 17:40:31 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 14 Feb 2015 16:40:31 +0000
Subject: [seqfan] A133058
Message-ID: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>

	I provided a Mma program and a b-file for the above sequence.
	Best,
	Harvey


From njasloane at gmail.com  Sat Feb 14 18:33:11 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Sat, 14 Feb 2015 12:33:11 -0500
Subject: [seqfan] Re: A133579
In-Reply-To: <CY1PR0401MB106882AC1B98B9DFA0598C2FC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
 <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
 <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>
 <CY1PR0401MB106882AC1B98B9DFA0598C2FC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
Message-ID: <CAAOnSgTWGu-YzW2uEPx-OGpN9eGYvh70sp+uirLexCwUUs3f5A@mail.gmail.com>

Harvey, Thanks for your work on A133580 and A133058.  As for A133579, I
corrected the terms and added a companion sequence A253092.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Feb 14, 2015 at 11:33 AM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         I checked the Mma programs for A133580 and they are still okay
> even after the offset was changed.  I recomputed the b-file to reflect the
> changed offset and the new b-file has now been uploaded.
>         I cannot generate the terms of A133579 even using Neil's revised
> definition so I suspect the revised definition is still not correct.
>         Best,
>         Harvey
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil
> Sloane
> Sent: Friday, February 13, 2015 9:22 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: A133579
>
> A133058 needed  a similar correction (and lacks a b-file - Harvey?)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 13, 2015 at 9:13 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > First, about A133580: the definition was correct, and the terms were
> > correct, but the offset should have been 0.  I changed the offset and
> > added some example lines to clarify the situation.
> >
> > The b-file is now wrong, unfortunately (Harvey, could you correct
> > it?), and probably the programs also need correcting.
> >
> > Following Franklin's hint, this suggests that the correct definition
> > of A133579 should be:
> >
> > a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime,
> > otherwise a(n) = a(n-1)/gcd(a(n-1),n).
> >
> > This almost matches the terms, but there is a mistake at a(6), I
> > believe, - as Harvey noticed - so it needs to be recomputed. (a(6)
> > should be 1 not 9). The offset is also wrong, it should be 0, and I
> > will fix that.
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters <
> > franktaw at netscape.net> wrote:
> >
> >> The definition is clearly wrong, since gcd(n,a(n-1)) always divides
> >> a(n-1).
> >>
> >> A133580 seems to be related, and may provide a clue. (BTW, the offset
> >> for
> >> A133580 is wrong; from the definition it should be 0.)
> >>
> >> Franklin T. Adams-Watters
> >>
> >>
> >> -----Original Message-----
> >> From: Harvey P. Dale <hpd at hpdale.org>
> >> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >> Sent: Fri, Feb 13, 2015 6:59 pm
> >> Subject: [seqfan] A133579
> >>
> >>
> >>         I cannot figure out how to generate the terms of the above
> >> sequence from its definition.
> >>         Best,
> >>         Harvey
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From hpd at hpdale.org  Sat Feb 14 19:26:30 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 14 Feb 2015 18:26:30 +0000
Subject: [seqfan] Re: A133579
In-Reply-To: <CAAOnSgTWGu-YzW2uEPx-OGpN9eGYvh70sp+uirLexCwUUs3f5A@mail.gmail.com>
References: <CY1PR0401MB1068E64A2FED1515ECA57AECC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <8D2160D583A7A09-1734-526E2@webmail-vm135.sysops.aol.com>
 <CAAOnSgTrUv0t1xwWzcMxAuMZ7rEA3sbwo6JV=HN0LvTRK3UBXw@mail.gmail.com>
 <CAAOnSgSZeWMVsMeUxx0_ssgs4AUCo7Ka0JeB4pZGTXCDxgU7Wg@mail.gmail.com>
 <CY1PR0401MB106882AC1B98B9DFA0598C2FC6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CAAOnSgTWGu-YzW2uEPx-OGpN9eGYvh70sp+uirLexCwUUs3f5A@mail.gmail.com>
Message-ID: <CY1PR0401MB1068D5C8635258D0EE276354C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>

Neil:
	I added a Mma program for each of A133579 and A253092 and a b-file for the former.
	Best,
	Harvey

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil Sloane
Sent: Saturday, February 14, 2015 12:33 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: A133579

Harvey, Thanks for your work on A133580 and A133058.  As for A133579, I corrected the terms and added a companion sequence A253092.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Feb 14, 2015 at 11:33 AM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         I checked the Mma programs for A133580 and they are still okay 
> even after the offset was changed.  I recomputed the b-file to reflect 
> the changed offset and the new b-file has now been uploaded.
>         I cannot generate the terms of A133579 even using Neil's 
> revised definition so I suspect the revised definition is still not correct.
>         Best,
>         Harvey
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil 
> Sloane
> Sent: Friday, February 13, 2015 9:22 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: A133579
>
> A133058 needed  a similar correction (and lacks a b-file - Harvey?)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 13, 2015 at 9:13 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > First, about A133580: the definition was correct, and the terms were 
> > correct, but the offset should have been 0.  I changed the offset 
> > and added some example lines to clarify the situation.
> >
> > The b-file is now wrong, unfortunately (Harvey, could you correct 
> > it?), and probably the programs also need correcting.
> >
> > Following Franklin's hint, this suggests that the correct definition 
> > of A133579 should be:
> >
> > a(0)=a(1)=1; for n>1, a(n) = 3*a(n-1)  if a(n-1) and n are coprime, 
> > otherwise a(n) = a(n-1)/gcd(a(n-1),n).
> >
> > This almost matches the terms, but there is a mistake at a(6), I 
> > believe, - as Harvey noticed - so it needs to be recomputed. (a(6) 
> > should be 1 not 9). The offset is also wrong, it should be 0, and I 
> > will fix that.
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Fri, Feb 13, 2015 at 8:33 PM, Frank Adams-Watters < 
> > franktaw at netscape.net> wrote:
> >
> >> The definition is clearly wrong, since gcd(n,a(n-1)) always divides 
> >> a(n-1).
> >>
> >> A133580 seems to be related, and may provide a clue. (BTW, the 
> >> offset for
> >> A133580 is wrong; from the definition it should be 0.)
> >>
> >> Franklin T. Adams-Watters
> >>
> >>
> >> -----Original Message-----
> >> From: Harvey P. Dale <hpd at hpdale.org>
> >> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> >> Sent: Fri, Feb 13, 2015 6:59 pm
> >> Subject: [seqfan] A133579
> >>
> >>
> >>         I cannot figure out how to generate the terms of the above 
> >> sequence from its definition.
> >>         Best,
> >>         Harvey
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >>
> >>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/

From arndt at jjj.de  Sat Feb 14 20:00:11 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Sat, 14 Feb 2015 20:00:11 +0100
Subject: [seqfan] Re: A marginal observation on some tables of R. H. Hardin
In-Reply-To: <CAAOnSgSSGykvFU3HHuuSDG0Ph6Scr6EA1nu_E54-THuT6QUEbQ@mail.gmail.com>
References: <1423656310.37806.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CABxCbJ029sjeFXNt=LjRjm7Sn17jnE5SmvvKKaULq8T2OdvpDQ@mail.gmail.com>
 <1423658073.83338.YahooMailNeo@web185003.mail.gq1.yahoo.com>
 <CAAOnSgThqyDTDvEoUt8xRp4CTWjsMjQO1jKTQLnJjvHbzLLavA@mail.gmail.com>
 <CAAkfSGKLSV546rm8w0=cQdFqcxnkgOeStMvh39mVO6kvkTAAQw@mail.gmail.com>
 <CAAOnSgRn6UUm8QYwooicnj09aSHpqT=U1js5V7UUE0kat=t=yw@mail.gmail.com>
 <8D2144BE3004646-B34-429C7@webmail-vm109.sysops.aol.com>
 <CAAOnSgRzuS9e9OaFTtXRLNhys_iR=SWWEDZXVE85S-fxGAsFnA@mail.gmail.com>
 <1423692357.25896.YahooMailNeo@web185002.mail.gq1.yahoo.com>
 <CAAOnSgSSGykvFU3HHuuSDG0Ph6Scr6EA1nu_E54-THuT6QUEbQ@mail.gmail.com>
Message-ID: <20150214190011.GA25417@jjj.de>

[I was biting my tongue up to here]

* Neil Sloane <njasloane at gmail.com> [Feb 12. 2015 08:19]:
> Good point, about discouraging human readers.
> 
> How about something like this? The machine-generated
> cross-references could say:
> 
> Cf. (generated automatically): A234111, A234112, ...

Yes!

There will be some draw backs, e.g., when people do the
A-number dance in the formula section, e.g., writing
A000040(n) for prime(n) or (much worse) A000027(n) for n.

And pretty please un-enforce the manual adding of all crossrefs.

Best,  jj


> 
> Best regards
> Neil
> 
> [...]


From acwacw at gmail.com  Sun Feb 15 00:51:34 2015
From: acwacw at gmail.com (Allan Wechsler)
Date: Sat, 14 Feb 2015 18:51:34 -0500
Subject: [seqfan] Re: A133058
In-Reply-To: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
References: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
Message-ID: <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>

If the program and b-file are right, the sequence enters a very simple
regime at n=638.
a(638+4k) = 1, a(639+4k) = 641+4k, a(640+4k) = 1282+8k, a(641+4k) = 2, for
all k>=0.

On Sat, Feb 14, 2015 at 11:40 AM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         I provided a Mma program and a b-file for the above sequence.
>         Best,
>         Harvey
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From oeis at hasler.fr  Sun Feb 15 15:04:28 2015
From: oeis at hasler.fr (M. F. Hasler)
Date: Sun, 15 Feb 2015 10:04:28 -0400
Subject: [seqfan] Re: A133058
In-Reply-To: <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>
References: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>
Message-ID: <CABxCbJ0QmaGjLidaDxs1kJ+1vXgQThnejJYj5YHmWcKH=cQuiA@mail.gmail.com>

On Sat, Feb 14, 2015 at 7:51 PM, Allan Wechsler <acwacw at gmail.com> wrote:
> If the program and b-file are right, the sequence enters a very simple
> regime at n=638.
> a(638+4k) = 1, a(639+4k) = 641+4k, a(640+4k) = 1282+8k, a(641+4k) = 2, for
> all k>=0.

I agree with Allan's result (and added PARI code producing the same sequence).
If one defines
a(1)=1; a(n+1) = a(n) + n + 1 if a(n) and n are coprime,
otherwise a(n+1) = a(n)/gcd(a(n),n).

one gets a "trivial" sequence having this behaviour right from the start :
 1, 3, 6, 2, 1, 7, 14, 2, 1, 11, 22, 2, 1, 15, 30, 2, 1, 19,...
i.e., a(4n+1) = 1, a(4n+2) = 4n+3, a(4n+3) = 8n+6, a(4n) = 2.

which I submitted in spite of "kw: easy, dumb" as A255051 ;
Changing the +1 to +2  yields yet another (less trivial) variant,
1, 4, 2, 7, 13, 20, 10, 19, 29, 40, 4, 17, 31, 46, 23, 40, 5, ...
submitted as A255140.
-- 
Maximilian


From acwacw at gmail.com  Sun Feb 15 15:30:38 2015
From: acwacw at gmail.com (Allan Wechsler)
Date: Sun, 15 Feb 2015 09:30:38 -0500
Subject: [seqfan] Re: A133058
In-Reply-To: <CABxCbJ0QmaGjLidaDxs1kJ+1vXgQThnejJYj5YHmWcKH=cQuiA@mail.gmail.com>
References: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>
 <CABxCbJ0QmaGjLidaDxs1kJ+1vXgQThnejJYj5YHmWcKH=cQuiA@mail.gmail.com>
Message-ID: <CADy-sGFUJeFF_Mscn-QrRkeh9JgEEcVit4FJZTBC3JqDP1DC+Q@mail.gmail.com>

A comment by the author (Zizka) seems to recognize the possibility of these
period-4 regimes. This leads me to think that one might devise a
meta-sequence telling how soon the regime is entered depending on starting
values.
On Feb 15, 2015 9:05 AM, "M. F. Hasler" <oeis at hasler.fr> wrote:

> On Sat, Feb 14, 2015 at 7:51 PM, Allan Wechsler <acwacw at gmail.com> wrote:
> > If the program and b-file are right, the sequence enters a very simple
> > regime at n=638.
> > a(638+4k) = 1, a(639+4k) = 641+4k, a(640+4k) = 1282+8k, a(641+4k) = 2,
> for
> > all k>=0.
>
> I agree with Allan's result (and added PARI code producing the same
> sequence).
> If one defines
> a(1)=1; a(n+1) = a(n) + n + 1 if a(n) and n are coprime,
> otherwise a(n+1) = a(n)/gcd(a(n),n).
>
> one gets a "trivial" sequence having this behaviour right from the start :
>  1, 3, 6, 2, 1, 7, 14, 2, 1, 11, 22, 2, 1, 15, 30, 2, 1, 19,...
> i.e., a(4n+1) = 1, a(4n+2) = 4n+3, a(4n+3) = 8n+6, a(4n) = 2.
>
> which I submitted in spite of "kw: easy, dumb" as A255051 ;
> Changing the +1 to +2  yields yet another (less trivial) variant,
> 1, 4, 2, 7, 13, 20, 10, 19, 29, 40, 4, 17, 31, 46, 23, 40, 5, ...
> submitted as A255140.
> --
> Maximilian
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From oeis at hasler.fr  Sun Feb 15 16:58:43 2015
From: oeis at hasler.fr (M. F. Hasler)
Date: Sun, 15 Feb 2015 11:58:43 -0400
Subject: [seqfan] Re: A133058
In-Reply-To: <CADy-sGFUJeFF_Mscn-QrRkeh9JgEEcVit4FJZTBC3JqDP1DC+Q@mail.gmail.com>
References: <CY1PR0401MB1068B25316419B52F57E3519C6200@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CADy-sGGV6d4ZpAQfmpwpN7VkiZn_NJ5aWxLKfvQoLC1-VCTfzg@mail.gmail.com>
 <CABxCbJ0QmaGjLidaDxs1kJ+1vXgQThnejJYj5YHmWcKH=cQuiA@mail.gmail.com>
 <CADy-sGFUJeFF_Mscn-QrRkeh9JgEEcVit4FJZTBC3JqDP1DC+Q@mail.gmail.com>
Message-ID: <CABxCbJ1cOna+cxC4OFq6YcEvxiSv6Cbo_5hm6eqnX_OqG507Ow@mail.gmail.com>

On Sun, Feb 15, 2015 at 10:30 AM, Allan Wechsler <acwacw at gmail.com> wrote:
> A comment by the author (Zizka) seems to recognize the possibility of these
> period-4 regimes. This leads me to think that one might devise a
> meta-sequence telling how soon the regime is entered depending on starting
> values.

Maybe, but note that A255140 enters a different loop, of form
(1,x,2x,x) and not (1,x,2x,2).
So actually we would have (at least) these 3 variants (**)
(with ...+n  vs. +n+1 and offset/indexing a[n-1] vs a[n])
and for each of these a meta sequence, function of the respective a[1].

(**) The a(n+1) = a(n)*2+1 resp. a(n)*3 variants do not have this
looping property, but each has its own self-similarity property, which
is for the latter also explained by the simple recurrence formula I
added for A253092 = log3 A133579.
-- 
Maximilian


From rhhardin at att.net  Mon Feb 16 17:22:52 2015
From: rhhardin at att.net (Ron Hardin)
Date: Mon, 16 Feb 2015 08:22:52 -0800
Subject: [seqfan] Guess the formula T(n,k)=?
Message-ID: <1424103772.41349.YahooMailNeo@web185002.mail.gq1.yahoo.com>

This is likely to be T(n,k)=f(n)+f(k) with f() having a 2^() flavor.


Every row, column and the diagonal satisfy the same recurrence.

The solutions seem to pick every 3rd row or column for 1's and sometimes add cross rows or columns of 1's.


/tmp/eyg
T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2

Table starts
..23..22..31..43..61..88.127.184.268.391.571..835.1222.1789.2620.3838.5623.8239
..22..28..37..49..67..94.133.190.274.397.577..841.1228.1795.2626.3844.5629.8245
..31..37..46..58..76.103.142.199.283.406.586..850.1237.1804.2635.3853.5638.8254
..43..49..58..70..88.115.154.211.295.418.598..862.1249.1816.2647.3865.5650.8266
..61..67..76..88.106.133.172.229.313.436.616..880.1267.1834.2665.3883.5668.8284
..88..94.103.115.133.160.199.256.340.463.643..907.1294.1861.2692.3910.5695.8311
.127.133.142.154.172.199.238.295.379.502.682..946.1333.1900.2731.3949.5734.8350
.184.190.199.211.229.256.295.352.436.559.739.1003.1390.1957.2788.4006.5791.8407
.268.274.283.295.313.340.379.436.520.643.823.1087.1474.2041.2872.4090.5875.8491
.391.397.406.418.436.463.502.559.643.766.946.1210.1597.2164.2995.4213.5998.8614

Empirical for diagonal:
a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4) for n>5
Empirical for column k:
k=1: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4) for n>5
k=2: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=3: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=4: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=5: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=6: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
k=7: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)

Two solutions for n=8 k=8
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....1..1..1..1..1..1..1..1..1..1
..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....1..1..1..1..1..1..1..1..1..1
..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0


 
rhhardin at mindspring.com
rhhardin at att.net (either)


From susanne.wienand at gmail.com  Tue Feb 17 23:05:43 2015
From: susanne.wienand at gmail.com (Susanne Wienand)
Date: Tue, 17 Feb 2015 23:05:43 +0100
Subject: [seqfan] Re: Guess the formula T(n,k)=?
In-Reply-To: <1424103772.41349.YahooMailNeo@web185002.mail.gq1.yahoo.com>
References: <1424103772.41349.YahooMailNeo@web185002.mail.gq1.yahoo.com>
Message-ID: <CAH=KaNvvbFoEeH8AvtEJc9MfYLhjuipHteVR+SaHHDgF5zw2_w@mail.gmail.com>

Hello Ron,

The terms seem to be related to A000930, Narayana's cow sequence.
If decreased by 22 and then divided by 3, the terms become

.1/3....0....3....7....13....22..35..54..82..123..183..271..400..589..866..1272..1867..2739

..0.....2....5....9....15....24..37..56..84..125..185..273..402..591..868..1274..1869..2741

..3.....5....8...12....18....27..40..59..87..128..188..276..405..594..871..1277..1872..2744

..7.....9...12...16....22....31..44..63..91..132..192..280..409..598..875..1281..1876..2748

.13....15...18...22....28....37..50..69..97..138..198..286..415..604..881..1287..1882..2754

.22....24...27...31....37....46..59..78.106..147..207..295..424..613..890..1296..1891..2763

.35....37...40...44....50....59..72..91.119..160..220..308..437..626..903..1309..1904..2776

.54....56...59...63....69....78..91.110.138..179..239..327..456..645..922..1328..1923..2795

.82....84...87...91....97...106.119.138.166..207..267..355..484..673..950..1356..1951..2823

123...125..128..132...138...147.160.179.207..248..308..396..525..714..991..1397..1992..2864

Most differences (except upper left corner) along the columns and the rows
seem to match with A000930:
*2*, *3*, *4*, *6*, *9*, *13*, *19*, *28*, 41, 60, 88, 129, 189, 277, 406,
595, 872, 1278

T(2,2) - T(2,1) = 2 - 0 = 2
T(2,3) - T(2,2) = 5 - 2 = 3
T(2,4) - T(2,3) = 9 - 5 = 4
...

I hope this can help to find the formula.

Regards
Susanne

2015-02-16 17:22 GMT+01:00 Ron Hardin <rhhardin at att.net>:

> This is likely to be T(n,k)=f(n)+f(k) with f() having a 2^() flavor.
>
>
> Every row, column and the diagonal satisfy the same recurrence.
>
> The solutions seem to pick every 3rd row or column for 1's and sometimes
> add cross rows or columns of 1's.
>
>
> /tmp/eyg
> T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum
> 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2
>
> Table starts
>
> ..23..22..31..43..61..88.127.184.268.391.571..835.1222.1789.2620.3838.5623.8239
>
> ..22..28..37..49..67..94.133.190.274.397.577..841.1228.1795.2626.3844.5629.8245
>
> ..31..37..46..58..76.103.142.199.283.406.586..850.1237.1804.2635.3853.5638.8254
>
> ..43..49..58..70..88.115.154.211.295.418.598..862.1249.1816.2647.3865.5650.8266
>
> ..61..67..76..88.106.133.172.229.313.436.616..880.1267.1834.2665.3883.5668.8284
>
> ..88..94.103.115.133.160.199.256.340.463.643..907.1294.1861.2692.3910.5695.8311
>
> .127.133.142.154.172.199.238.295.379.502.682..946.1333.1900.2731.3949.5734.8350
>
> .184.190.199.211.229.256.295.352.436.559.739.1003.1390.1957.2788.4006.5791.8407
>
> .268.274.283.295.313.340.379.436.520.643.823.1087.1474.2041.2872.4090.5875.8491
>
> .391.397.406.418.436.463.502.559.643.766.946.1210.1597.2164.2995.4213.5998.8614
>
> Empirical for diagonal:
> a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4) for n>5
> Empirical for column k:
> k=1: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4) for n>5
> k=2: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=3: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=4: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=5: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=6: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
> k=7: a(n)=2*a(n-1)-a(n-2)+a(n-3)-a(n-4)
>
> Two solutions for n=8 k=8
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
> ..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....1..1..1..1..1..1..1..1..1..1
> ..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....1..1..1..1..1..1..1..1..1..1
> ..1..1..1..1..1..1..1..1..1..1....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
> ..0..0..0..0..0..1..0..0..1..0....0..1..0..0..1..0..0..1..0..0
>
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From 2stepan at rambler.ru  Thu Feb 19 15:55:11 2015
From: 2stepan at rambler.ru (=?koi8-r?B?wNLJyiDHxdLB08nNz9c=?=)
Date: Thu, 19 Feb 2015 17:55:11 +0300
Subject: [seqfan] 4xy + 6x - 1
In-Reply-To: <1424357709.807527.19545.27241@mail.rambler.ru>
References: <1424357709.807527.19545.27241@mail.rambler.ru>
Message-ID: <1424357710.983999.15355.48162@mail.rambler.ru>


Dear SeqFans, 

Primes not of the form 4xy + 6x - 1: 2, 3, 7, 31, ...

What in the next one?

Thanks. JSG

From olivier.gerard at gmail.com  Thu Feb 19 16:56:24 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Thu, 19 Feb 2015 16:56:24 +0100
Subject: [seqfan] Re: 4xy + 6x - 1
In-Reply-To: <1424357710.983999.15355.48162@mail.rambler.ru>
References: <1424357709.807527.19545.27241@mail.rambler.ru>
 <1424357710.983999.15355.48162@mail.rambler.ru>
Message-ID: <CAAcpPSbcSpMF2jvhbMuMLJ7YdLeifK7RJWcmK4XQK67CSmGU0g@mail.gmail.com>

Youri,

If you restrict to x, y, 0 or positive integers,
your list is certainly 2 plus Mersenne primes,
anyway the next one should be 127.

If you allow x, y any integer, you will probably find
that only 2 cannot be represented this way.

Olivier


On Thu, Feb 19, 2015 at 3:55 PM, ???? ????????? <2stepan at rambler.ru> wrote:

>
> Dear SeqFans,
> Primes not of the form 4xy + 6x - 1: 2, 3, 7, 31, ...
>
> What in the next one?
>
> Thanks. JSG
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From rselcoe at entouchonline.net  Thu Feb 19 17:04:45 2015
From: rselcoe at entouchonline.net (Bob Selcoe)
Date: Thu, 19 Feb 2015 10:04:45 -0600
Subject: [seqfan] Re: 4xy + 6x - 1
In-Reply-To: <1424357710.983999.15355.48162@mail.rambler.ru>
References: <1424357709.807527.19545.27241@mail.rambler.ru>
 <1424357710.983999.15355.48162@mail.rambler.ru>
Message-ID: <37A5F4897FEB4645829AF7CB37B94C93@OwnerPC>

Hello,

127.  The sequence will be 2 and the Mersenne primes.  The equation is 
2x(2y+3)-1, which is all the even numbers times all the odd numbers minus 1. 
These are all the odd numbers except 2^n-1 which, when prime, are the 
Mersennes.

Best,
Bob Selcoe

--------------------------------------------------
From: "???? ?????????" <2stepan at rambler.ru>
Sent: Thursday, February 19, 2015 8:55 AM
To: <seqfan at list.seqfan.eu>
Subject: [seqfan] 4xy + 6x - 1

>
> Dear SeqFans,
> Primes not of the form 4xy + 6x - 1: 2, 3, 7, 31, ...
>
> What in the next one?
>
> Thanks. JSG
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
> 


From reddwarf2956 at yahoo.com  Fri Feb 20 10:53:42 2015
From: reddwarf2956 at yahoo.com (John W. Nicholson)
Date: Fri, 20 Feb 2015 09:53:42 +0000 (UTC)
Subject: [seqfan] Is there any problems with this proof?
Message-ID: <241484269.320541.1424426022835.JavaMail.yahoo@mail.yahoo.com>

Below is a proof based on A005250(n ) of the OEIS.? Can someone look at it and tell me if it true?
http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
If it is true, an edit of A005250 comments is needed.? 

Related:
https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1


?John W. Nicholson


From felix.froe at googlemail.com  Fri Feb 20 11:10:10 2015
From: felix.froe at googlemail.com (=?UTF-8?Q?Felix_Fr=C3=B6hlich?=)
Date: Fri, 20 Feb 2015 11:10:10 +0100
Subject: [seqfan] Additional keywords for OEIS
Message-ID: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>

Dear SeqFans,

as some of you might know, there has been some discussion about the
addition of additional keywords to the OEIS. Most of what I found regarding
that discussion has taken place in the userspace of Charles Greathouse in
the OEIS Wiki. See
https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and the
corresponding talk pages.

Personally I think the possibility to refine OEIS searches via specific
keywords is very useful and I often make use of that feature. The addition
of new keywords would allow one to get even more relevant results. For
example, Alex Ratushnyak in 2013 suggested the addition of a keyword 'prim'
that would allow one to find all sequences where all terms are prime. Two
obvious candidates for this keyword would be sequences like A000040
or A000043.

As I am not familiar with the technical aspects behind the OEIS database, I
would like to know how much work it would be to add new keywords to the
OEIS or whether it is technically possible at all (maybe it's just like
running an SQL query to update some database table, or maybe it requires
some complete rewrite of some part of the software underlying the OEIS, I
do not know). If it is technically feasible to do this and if those who
maintain the technical integrity of the OEIS think such a step would be
desirable, then as a next step we could collect suggestions regarding which
keywords would be useful.

What do others think?

Best regards

Felix Fr?hlich


From maximilian.hasler at gmail.com  Fri Feb 20 12:19:51 2015
From: maximilian.hasler at gmail.com (Maximilian F. Hasler)
Date: Fri, 20 Feb 2015 07:19:51 -0400
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
Message-ID: <CAOPi3QLUZDHy2CAgQ4j1UV1zCCbooqBJa=pOQbExrBE0KraOHw@mail.gmail.com>

I'm quite in favor of this, and more.
I developed some thoughts on
https://oeis.org/wiki/User:M._F._Hasler/Work_in_progress/Improvements_of_OEIS
I think switching to freely definable categories could be an interesting
alternative/complement to (or way of maintaining) the currently existing
index.

Maximilian
Le 20 f?vr. 2015 06:11, "Felix Fr?hlich" <felix.froe at googlemail.com> a
?crit :

> Dear SeqFans,
>
> as some of you might know, there has been some discussion about the
> addition of additional keywords to the OEIS. Most of what I found regarding
> that discussion has taken place in the userspace of Charles Greathouse in
> the OEIS Wiki. See
> https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and the
> corresponding talk pages.
>
> Personally I think the possibility to refine OEIS searches via specific
> keywords is very useful and I often make use of that feature. The addition
> of new keywords would allow one to get even more relevant results. For
> example, Alex Ratushnyak in 2013 suggested the addition of a keyword 'prim'
> that would allow one to find all sequences where all terms are prime. Two
> obvious candidates for this keyword would be sequences like A000040
> or A000043.
>
> As I am not familiar with the technical aspects behind the OEIS database, I
> would like to know how much work it would be to add new keywords to the
> OEIS or whether it is technically possible at all (maybe it's just like
> running an SQL query to update some database table, or maybe it requires
> some complete rewrite of some part of the software underlying the OEIS, I
> do not know). If it is technically feasible to do this and if those who
> maintain the technical integrity of the OEIS think such a step would be
> desirable, then as a next step we could collect suggestions regarding which
> keywords would be useful.
>
> What do others think?
>
> Best regards
>
> Felix Fr?hlich
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From franktaw at netscape.net  Fri Feb 20 19:18:04 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Fri, 20 Feb 2015 13:18:04 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
Message-ID: <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>

While I'm not familiar with the code being used, making new keywords 
available can't be very difficult.

Getting the keyword assigned to all and only those sequences where it 
belongs is another matter, ranging from a bit trickier than you might 
think to requiring many man-hours. For the example below, the process 
could be automated with 99%+ accuracy. I don't know of any off hand, 
but there are probably sequences in the database whose first non-prime 
member comes quite late. The process also has to be able to deal with 
sequences having very large terms. One keyword I have considered, 
"fact", for those sequences which depend on factorization, in the same 
way that "base" sequences depend on representation as numerals, would 
be very difficult to get anywhere close to being right.

Franklin T. Adams-Watters

-----Original Message-----
From: Felix Fr?hlich <felix.froe at googlemail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Feb 20, 2015 5:10 am
Subject: [seqfan] Additional keywords for OEIS


Dear SeqFans,

as some of you might know, there has been some discussion about the
addition of additional keywords to the OEIS. Most of what I found 
regarding
that discussion has taken place in the userspace of Charles Greathouse 
in
the OEIS Wiki. See
https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and 
the
corresponding talk pages.

Personally I think the possibility to refine OEIS searches via specific
keywords is very useful and I often make use of that feature. The 
addition
of new keywords would allow one to get even more relevant results. For
example, Alex Ratushnyak in 2013 suggested the addition of a keyword 
'prim'
that would allow one to find all sequences where all terms are prime. 
Two
obvious candidates for this keyword would be sequences like A000040
or A000043.

As I am not familiar with the technical aspects behind the OEIS 
database, I
would like to know how much work it would be to add new keywords to the
OEIS or whether it is technically possible at all (maybe it's just like
running an SQL query to update some database table, or maybe it requires
some complete rewrite of some part of the software underlying the OEIS, 
I
do not know). If it is technically feasible to do this and if those who
maintain the technical integrity of the OEIS think such a step would be
desirable, then as a next step we could collect suggestions regarding 
which
keywords would be useful.

What do others think?

Best regards

Felix Fr?hlich

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From njasloane at gmail.com  Fri Feb 20 18:24:10 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Fri, 20 Feb 2015 12:24:10 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
Message-ID: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>

Instead of adding more keywords, which are necessarily
rather limited, Charles and I had discussed adding
"categories".  This may be a better way to proceed.
Charles, did you think any more about how this idea might be implemented?
IIRC, you started to learn Go for that purpose?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> While I'm not familiar with the code being used, making new keywords
> available can't be very difficult.
>
> Getting the keyword assigned to all and only those sequences where it
> belongs is another matter, ranging from a bit trickier than you might think
> to requiring many man-hours. For the example below, the process could be
> automated with 99%+ accuracy. I don't know of any off hand, but there are
> probably sequences in the database whose first non-prime member comes quite
> late. The process also has to be able to deal with sequences having very
> large terms. One keyword I have considered, "fact", for those sequences
> which depend on factorization, in the same way that "base" sequences depend
> on representation as numerals, would be very difficult to get anywhere
> close to being right.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Felix Fr?hlich <felix.froe at googlemail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Feb 20, 2015 5:10 am
> Subject: [seqfan] Additional keywords for OEIS
>
>
> Dear SeqFans,
>
> as some of you might know, there has been some discussion about the
> addition of additional keywords to the OEIS. Most of what I found regarding
> that discussion has taken place in the userspace of Charles Greathouse in
> the OEIS Wiki. See
> https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and the
> corresponding talk pages.
>
> Personally I think the possibility to refine OEIS searches via specific
> keywords is very useful and I often make use of that feature. The addition
> of new keywords would allow one to get even more relevant results. For
> example, Alex Ratushnyak in 2013 suggested the addition of a keyword 'prim'
> that would allow one to find all sequences where all terms are prime. Two
> obvious candidates for this keyword would be sequences like A000040
> or A000043.
>
> As I am not familiar with the technical aspects behind the OEIS database, I
> would like to know how much work it would be to add new keywords to the
> OEIS or whether it is technically possible at all (maybe it's just like
> running an SQL query to update some database table, or maybe it requires
> some complete rewrite of some part of the software underlying the OEIS, I
> do not know). If it is technically feasible to do this and if those who
> maintain the technical integrity of the OEIS think such a step would be
> desirable, then as a next step we could collect suggestions regarding which
> keywords would be useful.
>
> What do others think?
>
> Best regards
>
> Felix Fr?hlich
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From franktaw at netscape.net  Fri Feb 20 19:36:26 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Fri, 20 Feb 2015 13:36:26 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
Message-ID: <8D21B4AE31E7FE1-23D4-8FBC5@webmail-vm077.sysops.aol.com>

I suggested some time ago linking keywords and the index. One would 
enter a "keyword" for the sequence, and this would automatically create 
an index entry for it. The keywords on search screens could then be 
live links to the index entries. (One would have to manually create the 
index entry itself and define its associated keyword.)

Franklin T. Adams-Watters

-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Feb 20, 2015 12:25 pm
Subject: [seqfan] Re: Additional keywords for OEIS


Instead of adding more keywords, which are necessarily
rather limited, Charles and I had discussed adding
"categories".  This may be a better way to proceed.
Charles, did you think any more about how this idea might be 
implemented?
IIRC, you started to learn Go for that purpose?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters 
<franktaw at netscape.net>
wrote:

> While I'm not familiar with the code being used, making new keywords
> available can't be very difficult.
>
> Getting the keyword assigned to all and only those sequences where it
> belongs is another matter, ranging from a bit trickier than you might 
think
> to requiring many man-hours. For the example below, the process could 
be
> automated with 99%+ accuracy. I don't know of any off hand, but there 
are
> probably sequences in the database whose first non-prime member comes 
quite
> late. The process also has to be able to deal with sequences having 
very
> large terms. One keyword I have considered, "fact", for those 
sequences
> which depend on factorization, in the same way that "base" sequences 
depend
> on representation as numerals, would be very difficult to get anywhere
> close to being right.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Felix Fr?hlich <felix.froe at googlemail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Feb 20, 2015 5:10 am
> Subject: [seqfan] Additional keywords for OEIS
>
>
> Dear SeqFans,
>
> as some of you might know, there has been some discussion about the
> addition of additional keywords to the OEIS. Most of what I found 
regarding
> that discussion has taken place in the userspace of Charles 
Greathouse in
> the OEIS Wiki. See
> https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and 
the
> corresponding talk pages.
>
> Personally I think the possibility to refine OEIS searches via 
specific
> keywords is very useful and I often make use of that feature. The 
addition
> of new keywords would allow one to get even more relevant results. For
> example, Alex Ratushnyak in 2013 suggested the addition of a keyword 
'prim'
> that would allow one to find all sequences where all terms are prime. 
Two
> obvious candidates for this keyword would be sequences like A000040
> or A000043.
>
> As I am not familiar with the technical aspects behind the OEIS 
database, I
> would like to know how much work it would be to add new keywords to 
the
> OEIS or whether it is technically possible at all (maybe it's just 
like
> running an SQL query to update some database table, or maybe it 
requires
> some complete rewrite of some part of the software underlying the 
OEIS, I
> do not know). If it is technically feasible to do this and if those 
who
> maintain the technical integrity of the OEIS think such a step would 
be
> desirable, then as a next step we could collect suggestions regarding 
which
> keywords would be useful.
>
> What do others think?
>
> Best regards
>
> Felix Fr?hlich
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From r.rosenthal at web.de  Fri Feb 20 20:30:19 2015
From: r.rosenthal at web.de (Rainer Rosenthal)
Date: Fri, 20 Feb 2015 20:30:19 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
Message-ID: <54E78B4B.8050303@web.de>

Am 20.02.2015 um 18:24 schrieb Neil Sloane:
> ... Charles and I had discussed adding "categories". 
> Charles, did you think any more about how this idea might be implemented?
> IIRC, you started to learn Go for that purpose?

What has the game of Go to do with this?
I love Go, so I am very interested.

Cheers,
Rainer




From jean-paul.allouche at imj-prg.fr  Fri Feb 20 20:37:12 2015
From: jean-paul.allouche at imj-prg.fr (jean-paul allouche)
Date: Fri, 20 Feb 2015 20:37:12 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <54E78B4B.8050303@web.de>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <54E78B4B.8050303@web.de>
Message-ID: <54E78CE8.2080909@imj-prg.fr>

Hi

Go is a programming language, see, e.g., https://golang.org
best
jean-paul


Le 20/02/15 20:30, Rainer Rosenthal a ?crit :
> Am 20.02.2015 um 18:24 schrieb Neil Sloane:
>> ... Charles and I had discussed adding "categories".
>> Charles, did you think any more about how this idea might be implemented?
>> IIRC, you started to learn Go for that purpose?
> What has the game of Go to do with this?
> I love Go, so I am very interested.
>
> Cheers,
> Rainer
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



From charles.greathouse at case.edu  Fri Feb 20 20:47:49 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Fri, 20 Feb 2015 14:47:49 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
Message-ID: <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>

I like the idea of new keywords, and I like the idea of categories.
Categories seem like a great solution to many problems because they would
be (by design) extendable. Unfortunately I haven't had time to look though
this part of Russ' code, but I intend to work on this eventually.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 12:24 PM, Neil Sloane <njasloane at gmail.com> wrote:

> Instead of adding more keywords, which are necessarily
> rather limited, Charles and I had discussed adding
> "categories".  This may be a better way to proceed.
> Charles, did you think any more about how this idea might be implemented?
> IIRC, you started to learn Go for that purpose?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <
> franktaw at netscape.net>
> wrote:
>
> > While I'm not familiar with the code being used, making new keywords
> > available can't be very difficult.
> >
> > Getting the keyword assigned to all and only those sequences where it
> > belongs is another matter, ranging from a bit trickier than you might
> think
> > to requiring many man-hours. For the example below, the process could be
> > automated with 99%+ accuracy. I don't know of any off hand, but there are
> > probably sequences in the database whose first non-prime member comes
> quite
> > late. The process also has to be able to deal with sequences having very
> > large terms. One keyword I have considered, "fact", for those sequences
> > which depend on factorization, in the same way that "base" sequences
> depend
> > on representation as numerals, would be very difficult to get anywhere
> > close to being right.
> >
> > Franklin T. Adams-Watters
> >
> >
> > -----Original Message-----
> > From: Felix Fr?hlich <felix.froe at googlemail.com>
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Sent: Fri, Feb 20, 2015 5:10 am
> > Subject: [seqfan] Additional keywords for OEIS
> >
> >
> > Dear SeqFans,
> >
> > as some of you might know, there has been some discussion about the
> > addition of additional keywords to the OEIS. Most of what I found
> regarding
> > that discussion has taken place in the userspace of Charles Greathouse in
> > the OEIS Wiki. See
> > https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> > https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and
> the
> > corresponding talk pages.
> >
> > Personally I think the possibility to refine OEIS searches via specific
> > keywords is very useful and I often make use of that feature. The
> addition
> > of new keywords would allow one to get even more relevant results. For
> > example, Alex Ratushnyak in 2013 suggested the addition of a keyword
> 'prim'
> > that would allow one to find all sequences where all terms are prime. Two
> > obvious candidates for this keyword would be sequences like A000040
> > or A000043.
> >
> > As I am not familiar with the technical aspects behind the OEIS
> database, I
> > would like to know how much work it would be to add new keywords to the
> > OEIS or whether it is technically possible at all (maybe it's just like
> > running an SQL query to update some database table, or maybe it requires
> > some complete rewrite of some part of the software underlying the OEIS, I
> > do not know). If it is technically feasible to do this and if those who
> > maintain the technical integrity of the OEIS think such a step would be
> > desirable, then as a next step we could collect suggestions regarding
> which
> > keywords would be useful.
> >
> > What do others think?
> >
> > Best regards
> >
> > Felix Fr?hlich
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From charles.greathouse at case.edu  Fri Feb 20 23:24:17 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Fri, 20 Feb 2015 17:24:17 -0500
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <241484269.320541.1424426022835.JavaMail.yahoo@mail.yahoo.com>
References: <241484269.320541.1424426022835.JavaMail.yahoo@mail.yahoo.com>
Message-ID: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>

I suspect that there is some k > 1 such that the ratio is greater than k
infinitely often. Is anyone interested in crunching the numbers here on the
heuristic?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <reddwarf2956 at yahoo.com>
wrote:

> Below is a proof based on A005250(n ) of the OEIS.  Can someone look at it
> and tell me if it true?
>
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> If it is true, an edit of A005250 comments is needed.
>
> Related:
>
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
>
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
>
>
>  John W. Nicholson
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From reddwarf2956 at yahoo.com  Sat Feb 21 01:58:06 2015
From: reddwarf2956 at yahoo.com (John W. Nicholson)
Date: Sat, 21 Feb 2015 00:58:06 +0000 (UTC)
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>
References: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>
Message-ID: <422736994.5533162.1424480286641.JavaMail.yahoo@mail.yahoo.com>

Charles, 

Does that mean that the proof with first question, that the ratio <=2, is correct and with out problems so that you are now looking at the second question with the limit of the ratio going to infinity =1??John W. Nicholson 

     On Friday, February 20, 2015 4:24 PM, Charles Greathouse <charles.greathouse at case.edu> wrote:
   
 

 I suspect that there is some k > 1 such that the ratio is greater than k
infinitely often. Is anyone interested in crunching the numbers here on the
heuristic?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <reddwarf2956 at yahoo.com>
wrote:

> Below is a proof based on A005250(n ) of the OEIS.? Can someone look at it
> and tell me if it true?
>
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> If it is true, an edit of A005250 comments is needed.
>
> Related:
>
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
>
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
>
>
>? John W. Nicholson
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


 
   


From seqfan at matcos.nl  Fri Feb 20 21:59:05 2015
From: seqfan at matcos.nl (Matthijs Coster)
Date: Fri, 20 Feb 2015 21:59:05 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
Message-ID: <54E7A019.2050006@matcos.nl>

I would like keywords such that only sequences can be searched which are 
increasing, non decreasing, consist of different integers. That would be 
wonderful!

Matthijs Coster

Charles Greathouse schreef op 20-2-2015 om 20:47:
> I like the idea of new keywords, and I like the idea of categories.
> Categories seem like a great solution to many problems because they would
> be (by design) extendable. Unfortunately I haven't had time to look though
> this part of Russ' code, but I intend to work on this eventually.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 12:24 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
>> Instead of adding more keywords, which are necessarily
>> rather limited, Charles and I had discussed adding
>> "categories".  This may be a better way to proceed.
>> Charles, did you think any more about how this idea might be implemented?
>> IIRC, you started to learn Go for that purpose?
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <
>> franktaw at netscape.net>
>> wrote:
>>
>>> While I'm not familiar with the code being used, making new keywords
>>> available can't be very difficult.
>>>
>>> Getting the keyword assigned to all and only those sequences where it
>>> belongs is another matter, ranging from a bit trickier than you might
>> think
>>> to requiring many man-hours. For the example below, the process could be
>>> automated with 99%+ accuracy. I don't know of any off hand, but there are
>>> probably sequences in the database whose first non-prime member comes
>> quite
>>> late. The process also has to be able to deal with sequences having very
>>> large terms. One keyword I have considered, "fact", for those sequences
>>> which depend on factorization, in the same way that "base" sequences
>> depend
>>> on representation as numerals, would be very difficult to get anywhere
>>> close to being right.
>>>
>>> Franklin T. Adams-Watters
>>>
>>>
>>> -----Original Message-----
>>> From: Felix Fr?hlich <felix.froe at googlemail.com>
>>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>> Sent: Fri, Feb 20, 2015 5:10 am
>>> Subject: [seqfan] Additional keywords for OEIS
>>>
>>>
>>> Dear SeqFans,
>>>
>>> as some of you might know, there has been some discussion about the
>>> addition of additional keywords to the OEIS. Most of what I found
>> regarding
>>> that discussion has taken place in the userspace of Charles Greathouse in
>>> the OEIS Wiki. See
>>> https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
>>> https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table and
>> the
>>> corresponding talk pages.
>>>
>>> Personally I think the possibility to refine OEIS searches via specific
>>> keywords is very useful and I often make use of that feature. The
>> addition
>>> of new keywords would allow one to get even more relevant results. For
>>> example, Alex Ratushnyak in 2013 suggested the addition of a keyword
>> 'prim'
>>> that would allow one to find all sequences where all terms are prime. Two
>>> obvious candidates for this keyword would be sequences like A000040
>>> or A000043.
>>>
>>> As I am not familiar with the technical aspects behind the OEIS
>> database, I
>>> would like to know how much work it would be to add new keywords to the
>>> OEIS or whether it is technically possible at all (maybe it's just like
>>> running an SQL query to update some database table, or maybe it requires
>>> some complete rewrite of some part of the software underlying the OEIS, I
>>> do not know). If it is technically feasible to do this and if those who
>>> maintain the technical integrity of the OEIS think such a step would be
>>> desirable, then as a next step we could collect suggestions regarding
>> which
>>> keywords would be useful.
>>>
>>> What do others think?
>>>
>>> Best regards
>>>
>>> Felix Fr?hlich
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



From franktaw at netscape.net  Sat Feb 21 08:33:05 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Sat, 21 Feb 2015 02:33:05 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
Message-ID: <8D21BBFC3FD21B5-1B58-8EB7A@webmail-va170.sysops.aol.com>

I don't know what you mean by categories. Is there a reference to this 
in the Wiki?

Franklin T. Adams-Watters

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Feb 20, 2015 1:48 pm
Subject: [seqfan] Re: Additional keywords for OEIS


I like the idea of new keywords, and I like the idea of categories.
Categories seem like a great solution to many problems because they 
would
be (by design) extendable. Unfortunately I haven't had time to look 
though
this part of Russ' code, but I intend to work on this eventually.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 12:24 PM, Neil Sloane <njasloane at gmail.com> 
wrote:

> Instead of adding more keywords, which are necessarily
> rather limited, Charles and I had discussed adding
> "categories".  This may be a better way to proceed.
> Charles, did you think any more about how this idea might be 
implemented?
> IIRC, you started to learn Go for that purpose?
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <
> franktaw at netscape.net>
> wrote:
>
> > While I'm not familiar with the code being used, making new keywords
> > available can't be very difficult.
> >
> > Getting the keyword assigned to all and only those sequences where 
it
> > belongs is another matter, ranging from a bit trickier than you 
might
> think
> > to requiring many man-hours. For the example below, the process 
could be
> > automated with 99%+ accuracy. I don't know of any off hand, but 
there are
> > probably sequences in the database whose first non-prime member 
comes
> quite
> > late. The process also has to be able to deal with sequences having 
very
> > large terms. One keyword I have considered, "fact", for those 
sequences
> > which depend on factorization, in the same way that "base" sequences
> depend
> > on representation as numerals, would be very difficult to get 
anywhere
> > close to being right.
> >
> > Franklin T. Adams-Watters
> >
> >
> > -----Original Message-----
> > From: Felix Fr?hlich <felix.froe at googlemail.com>
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Sent: Fri, Feb 20, 2015 5:10 am
> > Subject: [seqfan] Additional keywords for OEIS
> >
> >
> > Dear SeqFans,
> >
> > as some of you might know, there has been some discussion about the
> > addition of additional keywords to the OEIS. Most of what I found
> regarding
> > that discussion has taken place in the userspace of Charles 
Greathouse in
> > the OEIS Wiki. See
> > https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
> > https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table 
and
> the
> > corresponding talk pages.
> >
> > Personally I think the possibility to refine OEIS searches via 
specific
> > keywords is very useful and I often make use of that feature. The
> addition
> > of new keywords would allow one to get even more relevant results. 
For
> > example, Alex Ratushnyak in 2013 suggested the addition of a keyword
> 'prim'
> > that would allow one to find all sequences where all terms are 
prime. Two
> > obvious candidates for this keyword would be sequences like A000040
> > or A000043.
> >
> > As I am not familiar with the technical aspects behind the OEIS
> database, I
> > would like to know how much work it would be to add new keywords to 
the
> > OEIS or whether it is technically possible at all (maybe it's just 
like
> > running an SQL query to update some database table, or maybe it 
requires
> > some complete rewrite of some part of the software underlying the 
OEIS, I
> > do not know). If it is technically feasible to do this and if those 
who
> > maintain the technical integrity of the OEIS think such a step 
would be
> > desirable, then as a next step we could collect suggestions 
regarding
> which
> > keywords would be useful.
> >
> > What do others think?
> >
> > Best regards
> >
> > Felix Fr?hlich
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From felix.froe at googlemail.com  Sat Feb 21 09:08:53 2015
From: felix.froe at googlemail.com (=?UTF-8?Q?Felix_Fr=C3=B6hlich?=)
Date: Sat, 21 Feb 2015 09:08:53 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <8D21BBFC3FD21B5-1B58-8EB7A@webmail-va170.sysops.aol.com>
References: <CAGtmjtRexzfY4ZzqQ8BDSNVqHoj4gmXNLow_BzPoCDHd2trVTw@mail.gmail.com>
 <8D21B4852507389-23D4-8F917@webmail-vm077.sysops.aol.com>
 <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <CAAkfSGLX5XjO2wOfMWeoojUgzDNzhXAshRbQg4hcm1AM89OyHw@mail.gmail.com>
 <8D21BBFC3FD21B5-1B58-8EB7A@webmail-va170.sysops.aol.com>
Message-ID: <CAGtmjtQBAsABRZ91VUACbMc4Z2yUfMB=c26vgEDSEqDwV-tdew@mail.gmail.com>

I don't think there is a reference in the OEIS wiki, but for a general
overview of what I believe Neil is referring to above, see
http://www.mediawiki.org/wiki/Help:Categories.

Felix

2015-02-21 8:33 GMT+01:00 Frank Adams-Watters <franktaw at netscape.net>:

> I don't know what you mean by categories. Is there a reference to this in
> the Wiki?
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Charles Greathouse <charles.greathouse at case.edu>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Feb 20, 2015 1:48 pm
> Subject: [seqfan] Re: Additional keywords for OEIS
>
>
> I like the idea of new keywords, and I like the idea of categories.
> Categories seem like a great solution to many problems because they would
> be (by design) extendable. Unfortunately I haven't had time to look though
> this part of Russ' code, but I intend to work on this eventually.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 12:24 PM, Neil Sloane <njasloane at gmail.com> wrote:
>
>  Instead of adding more keywords, which are necessarily
>> rather limited, Charles and I had discussed adding
>> "categories".  This may be a better way to proceed.
>> Charles, did you think any more about how this idea might be
>>
> implemented?
>
>> IIRC, you started to learn Go for that purpose?
>>
>> Best regards
>> Neil
>>
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
>>
> NJ.
>
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>>
>>
>> On Fri, Feb 20, 2015 at 1:18 PM, Frank Adams-Watters <
>> franktaw at netscape.net>
>> wrote:
>>
>> > While I'm not familiar with the code being used, making new keywords
>> > available can't be very difficult.
>> >
>> > Getting the keyword assigned to all and only those sequences where
>>
> it
>
>> > belongs is another matter, ranging from a bit trickier than you
>>
> might
>
>> think
>> > to requiring many man-hours. For the example below, the process
>>
> could be
>
>> > automated with 99%+ accuracy. I don't know of any off hand, but
>>
> there are
>
>> > probably sequences in the database whose first non-prime member
>>
> comes
>
>> quite
>> > late. The process also has to be able to deal with sequences having
>>
> very
>
>> > large terms. One keyword I have considered, "fact", for those
>>
> sequences
>
>> > which depend on factorization, in the same way that "base" sequences
>> depend
>> > on representation as numerals, would be very difficult to get
>>
> anywhere
>
>> > close to being right.
>> >
>> > Franklin T. Adams-Watters
>> >
>> >
>> > -----Original Message-----
>> > From: Felix Fr?hlich <felix.froe at googlemail.com>
>> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>> > Sent: Fri, Feb 20, 2015 5:10 am
>> > Subject: [seqfan] Additional keywords for OEIS
>> >
>> >
>> > Dear SeqFans,
>> >
>> > as some of you might know, there has been some discussion about the
>> > addition of additional keywords to the OEIS. Most of what I found
>> regarding
>> > that discussion has taken place in the userspace of Charles
>>
> Greathouse in
>
>> > the OEIS Wiki. See
>> > https://oeis.org/wiki/User_talk:Charles_R_Greathouse_IV/Keywords and
>> > https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Keywords/Table
>>
> and
>
>> the
>> > corresponding talk pages.
>> >
>> > Personally I think the possibility to refine OEIS searches via
>>
> specific
>
>> > keywords is very useful and I often make use of that feature. The
>> addition
>> > of new keywords would allow one to get even more relevant results.
>>
> For
>
>> > example, Alex Ratushnyak in 2013 suggested the addition of a keyword
>> 'prim'
>> > that would allow one to find all sequences where all terms are
>>
> prime. Two
>
>> > obvious candidates for this keyword would be sequences like A000040
>> > or A000043.
>> >
>> > As I am not familiar with the technical aspects behind the OEIS
>> database, I
>> > would like to know how much work it would be to add new keywords to
>>
> the
>
>> > OEIS or whether it is technically possible at all (maybe it's just
>>
> like
>
>> > running an SQL query to update some database table, or maybe it
>>
> requires
>
>> > some complete rewrite of some part of the software underlying the
>>
> OEIS, I
>
>> > do not know). If it is technically feasible to do this and if those
>>
> who
>
>> > maintain the technical integrity of the OEIS think such a step
>>
> would be
>
>> > desirable, then as a next step we could collect suggestions
>>
> regarding
>
>> which
>> > keywords would be useful.
>> >
>> > What do others think?
>> >
>> > Best regards
>> >
>> > Felix Fr?hlich
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>> >
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From zbi74583.boat at orange.zero.jp  Sat Feb 21 08:19:14 2015
From: zbi74583.boat at orange.zero.jp (zbi74583.boat at orange.zero.jp)
Date: Sat, 21 Feb 2015 16:19:14 +0900 (JST)
Subject: [seqfan] Re: Generalized Amicable Number
Message-ID: <62970.111.188.22.63.1424503154.squirrel@webmail.zero.jp>

    Hi,Jack
    Thank you for confirming and computing more terms

    The first number was the following

    x = 5^3*11^2*13*131*2^2*3^2
    y = 5^3*11^2*13*131*7^2

    I am sorry that I wrote a wrong number which I wrote on next line in my note
book
    Could you confirm it?



    I am now computing the numbers which satisfy the following

    F(x)=F(y)=m/n*(x*y)^(1/2)

    Where F(k) is one of the divisor function, both m,n are small

    Here is an interesting example

    UnitaryPhi(x)=UnitaryPhi(y)=m/n*(x*y)^(1/2)

    m/n=3/4    A143649
    x = 2^10*5*3^2*11^2
    y = 2^10*5*31^2
    Is it tenth term?

    m/n=4/5
    x = y = 5

    x = 2^2*3^2
    y = 5^2

    x = 5^4*7*2^10*3^8*11^2*41^2
    y = 5^4*7*2^20*3^2*13^2*31^2

    Could you confirm them and compute more terms?



    >(-1)Sigma(x)=(-1)Sigma(y)=8/5*(x*y)^(1/2)

    >The definition of (-1)Sigma(x) is here A049060



    Yasutoshi




From charles.greathouse at case.edu  Sat Feb 21 16:42:35 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Sat, 21 Feb 2015 10:42:35 -0500
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <422736994.5533162.1424480286641.JavaMail.yahoo@mail.yahoo.com>
References: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>
 <422736994.5533162.1424480286641.JavaMail.yahoo@mail.yahoo.com>
Message-ID: <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>

I don't know what to think of the first question. It's numerically
unassailable -- to build up evidence in the primes, one way or another,
you'd probably need to get a lot closer to a googolplex than a googol, and
even 10^20 is out of reach at the moment. The only recourse I see is
checking whether it holds in the Cramer model, flawed as it is.

It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
also wouldn't surprise me if it happened only finitely often.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com>
wrote:

> Charles,
>
> Does that mean that the proof with first question, that the ratio <=2, is
> correct and with out problems so that you are now looking at the second
> question with the limit of the ratio going to infinity =1? John W. Nicholson
>
>      On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>
>
>  I suspect that there is some k > 1 such that the ratio is greater than k
> infinitely often. Is anyone interested in crunching the numbers here on the
> heuristic?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Below is a proof based on A005250(n ) of the OEIS.  Can someone look at
> it
> > and tell me if it true?
> >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > If it is true, an edit of A005250 comments is needed.
> >
> > Related:
> >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> >
> >
> >  John W. Nicholson
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From reddwarf2956 at yahoo.com  Sat Feb 21 19:05:18 2015
From: reddwarf2956 at yahoo.com (John W. Nicholson)
Date: Sat, 21 Feb 2015 18:05:18 +0000 (UTC)
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>
References: <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>
Message-ID: <1727707214.931670.1424541918410.JavaMail.yahoo@mail.yahoo.com>

"It's numerically unassailable"? Please, do explain, because I do not see how it is a problem when I used Ramanujan primes, the RPC, and subsutution to limit the size of the gaps. I don't see how this is different for a large maximal gap too.
?John W. Nicholson 

     On Saturday, February 21, 2015 9:43 AM, Charles Greathouse <charles.greathouse at case.edu> wrote:
   
 

 I don't know what to think of the first question. It's numerically
unassailable -- to build up evidence in the primes, one way or another,
you'd probably need to get a lot closer to a googolplex than a googol, and
even 10^20 is out of reach at the moment. The only recourse I see is
checking whether it holds in the Cramer model, flawed as it is.

It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
also wouldn't surprise me if it happened only finitely often.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com>
wrote:

> Charles,
>
> Does that mean that the proof with first question, that the ratio <=2, is
> correct and with out problems so that you are now looking at the second
> question with the limit of the ratio going to infinity =1? John W. Nicholson
>
>? ? ? On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>
>
>? I suspect that there is some k > 1 such that the ratio is greater than k
> infinitely often. Is anyone interested in crunching the numbers here on the
> heuristic?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Below is a proof based on A005250(n ) of the OEIS.? Can someone look at
> it
> > and tell me if it true?
> >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > If it is true, an edit of A005250 comments is needed.
> >
> > Related:
> >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> >
> >
> >? John W. Nicholson
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


 
   


From zbi74583.boat at orange.zero.jp  Sat Feb 21 08:28:54 2015
From: zbi74583.boat at orange.zero.jp (zbi74583.boat at orange.zero.jp)
Date: Sat, 21 Feb 2015 16:28:54 +0900 (JST)
Subject: [seqfan] Song of Integer
Message-ID: <62987.111.188.22.63.1424503734.squirrel@webmail.zero.jp>

    Hi,Seqfans

    Do you know "BABYMETAL" who is a girl  matal band?
    Their album got top of World Albums in Billboard of USA
    "Megitsune"

    https://www.youtube.com/watch?v=cK3NMZAUKGw

    They also sing a song of "Integer"
    "4 No Uta" which means "Song of four"
    Live in London

    https://www.youtube.com/watch?v=chYaUGOTo3I

    Lylic of the song

    https://www.youtube.com/watch?v=ASyqaP6dguA

    Two younger members of them wrote it when they were twelve years old
    I think they are so smart



    Yasutoshi




From olivier.gerard at gmail.com  Sun Feb 22 00:51:07 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Sun, 22 Feb 2015 00:51:07 +0100
Subject: [seqfan] Fwd : House of Graphs: a database of interesting graphs --
	an update
Message-ID: <CAAcpPSZ5vW1BJrRGYittRnqMDHt=o74TjJoqXiSzvj33d=PCLg@mail.gmail.com>

This might be of interest to several seqfan members.

With my best regards,

Olivier G?rard



---------- Forwarded message ----------
From: Jan Goedgebeur <jan.goedgebeur at ugent.be>
Date: Tue, Feb 17, 2015 at 2:46 PM


Already in 2012 we announced the website "House of Graphs" --
http://hog.grinvin.org/ . In the meantime several new lists of graphs,
"interesting graphs", and invariants have been added to the website.

"House of Graphs" hosts lists of graphs (like Snarks, Fullerenes, etc.) and
links to other pages with lists of combinatorial structures (like vertex
transitive graphs, Ramsey graphs, etc.). But its main feature is a
searchable database of graphs that already occurred as counterexamples to
conjectures, as extremal graphs or in other contexts. In short we call this
the database of "interesting graphs".

The key idea is that although already for small vertex numbers extremely
many graphs exist, there are some that serve again and again as
counterexamples and that a database of these graphs should be established.
In this database one can e.g. search for graphs with certain invariant
values, graphs with a certain name (e.g. Petersen, Heawood, Balaban, etc.)
or graphs that are marked as being interesting for a certain invariant
(e.g. marked as being interesting for the girth). These searches can of
course also be combined and the results downloaded so that one gets good
candidates for testing new conjectures one is working on.

Users can also add graphs to the database. If the graphs are not yet in the
database, the system computes invariant values for the graphs. So the
database can also be used as a repository. If you discover new interesting
graphs, you can make them available to other users by submitting them to
the database together with a text identifier (e.g.
counterexample_this_conjecture).
Then other scientists can find and download the graph from "House of
Graphs".

More information on "House of Graphs" and its functionalities is given in:

Discrete Applied Mathematics, Volume 161, Issues 1-2, Jan. 2013, pages
311-314
Available online: http://dx.doi.org/10.1016/j.dam.2012.07.018

and

http://arxiv.org/abs/1204.3549

while "House of Graphs" can be accessed at: http://hog.grinvin.org/


Gunnar Brinkmann, Kris Coolsaet, Jan Goedgebeur and Hadrien Melot

-- 

Jan Goedgebeur
Applied Mathematics and Computer Science
Ghent University
Krijgslaan 281 - S9
B - 9000 Ghent


From pew at worldwidemann.com  Sun Feb 22 22:29:17 2015
From: pew at worldwidemann.com (Philipp Emanuel Weidmann)
Date: Sun, 22 Feb 2015 22:29:17 +0100
Subject: [seqfan] Purely algorithmic number sequence identification
Message-ID: <1424640557.3507.31.camel@worldwidemann.com>

I have been experimenting with a purely algorithmic (brute force)
approach to the question "which formula generates this number
sequence?", designed to complement existing systems based on database
lookups (OEIS) and pattern transforms (Mathematica).

The system developed for that purpose is now available, both as a
library/executable JAR (https://github.com/p-e-w/sequencer) and as a
simple (beta stage) web service (http://www.sequenceboss.org/).

At its core, Sequencer is a tree-based expression generator plus a
hybrid search engine combining a fast numerical pre-checker with a
symbolic verifier. Because the numerical checker is so fast, expressions
of relatively high complexity (7-8 nodes) can be exhaustively searched
in minutes on commodity hardware to check whether they generate the
given numbers.

Despite its early stage of development, Sequencer can already identify
(i.e. find a closed form expression for) many sequences that OEIS,
Superseeker and Mathematica can not. It is particularly strong at
finding complex, nonlinear or inhomogeneous recurrence relations like

  a(1) = 1
  a(2) = 1
  a(3) = 1
  a(n) = a(n-2)^2+a(n-1)+a(n-3)   for n >= 4

when provided the sequence

  1, 1, 1, 3, 5, 15, 43, 273

something which none of the above mentioned systems is currently able to
do. But the system can also quickly find unusual, relatively simple
general terms for sequences like

  11, 47, 123, 214, 257

for which Sequencer returns

  a(n) = n + Binomial(10,n)

in less than one second (http://www.sequenceboss.org/?q=11%2C+47%2C+123%
2C+214%2C+257).

By leveraging the Symja computer algebra system, Sequencer supports
fully symbolic input and output and is not limited to integer sequences.
For example, running the program on the input

  0, 1/2, sqrt(3)/2, 1

produces (search depth 6) the formula

  a(n) = Sin(1/6*Pi*(n-1))


I invite you to give the Sequencer/SequenceBoss system a try. If you are
familiar with Scala, you will find it easy to modify the
FormulaGenerator class to expand the range of expressions that can be
searched beyond what the command line switches already offer. Next in
line I plan to add multicore support based on Scala Actors which should
almost multiply the current search performance by the number of
available CPU cores as the search is efficiently parallelizable. Bug
reports and code contributions are very welcome, ideally on GitHub.

Best regards

Philipp Emanuel Weidmann




From akourbatov at gmail.com  Sun Feb 22 23:04:10 2015
From: akourbatov at gmail.com (Alexei Kourbatov)
Date: Sun, 22 Feb 2015 14:04:10 -0800
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>
References: <CAAkfSGLVkwjB9H-HxKp6rfTxbgu6M0v1J07GFoMzSBYoADMvuA@mail.gmail.com>
 <422736994.5533162.1424480286641.JavaMail.yahoo@mail.yahoo.com>
 <CAAkfSGLTd61GELymO-1BctT3Y_N2OYKcouZ2yubxv_rjcj9xeQ@mail.gmail.com>
Message-ID: <CAE3sB-CuevC0dyw7c-uut2NVDBdbCuKRj2uyS74GdST0uR=MVw@mail.gmail.com>

In Cramer's model, I feel that both statements are true with probability 1.

In the original proof, the last sentence "So the gap g_y ..." apparently
does not follow from the preceding statements (as far as I can tell).
To illustrate my point: a-c < 2(b-d) does not follow from { a < 2b and c <
2d} - but it would follow e.g. from { a < 2b and c >= 2d}



On Sat, Feb 21, 2015 at 7:42 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> I don't know what to think of the first question. It's numerically
> unassailable -- to build up evidence in the primes, one way or another,
> you'd probably need to get a lot closer to a googolplex than a googol, and
> even 10^20 is out of reach at the moment. The only recourse I see is
> checking whether it holds in the Cramer model, flawed as it is.
>
> It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
> also wouldn't surprise me if it happened only finitely often.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Charles,
> >
> > Does that mean that the proof with first question, that the ratio <=2, is
> > correct and with out problems so that you are now looking at the second
> > question with the limit of the ratio going to infinity =1? John W.
> Nicholson
> >
> >      On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> > charles.greathouse at case.edu> wrote:
> >
> >
> >
> >  I suspect that there is some k > 1 such that the ratio is greater than k
> > infinitely often. Is anyone interested in crunching the numbers here on
> the
> > heuristic?
> >
> > Charles Greathouse
> > Analyst/Programmer
> > Case Western Reserve University
> >
> > On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <
> reddwarf2956 at yahoo.com
> > >
> > wrote:
> >
> > > Below is a proof based on A005250(n ) of the OEIS.  Can someone look at
> > it
> > > and tell me if it true?
> > >
> > >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > > If it is true, an edit of A005250 comments is needed.
> > >
> > > Related:
> > >
> > >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> > >
> > >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> > >
> > >
> > >  John W. Nicholson
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From olivier.gerard at gmail.com  Mon Feb 23 11:42:45 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Mon, 23 Feb 2015 11:42:45 +0100
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <1424640557.3507.31.camel@worldwidemann.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
Message-ID: <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>

Dear Philipp Emmanuel,

your program Sequencer is really interesting. In spirit, one can say it is
close to
Robert Munafo's RIES

http://mrob.com/pub/ries/index.html

but for integer sequences

It would be nice to test it on "hard" sequences and other sequences without
formula.

I have a first candidate (which is inspired by the same kind of brute force
exploration)

https://oeis.org/A229673

"The number of subsets of nonzero integers of cardinality n, produced as
the steps in a computation starting with 1 and using the operations of
multiplication, addition, or subtraction."

1, 3, 15, 126, 1667, 31966, 828678, 27535826, 1128945382, ...

Best regards,

Olivier


On Sun, Feb 22, 2015 at 10:29 PM, Philipp Emanuel Weidmann <
pew at worldwidemann.com> wrote:

> I have been experimenting with a purely algorithmic (brute force)
> approach to the question "which formula generates this number
> sequence?", designed to complement existing systems based on database
> lookups (OEIS) and pattern transforms (Mathematica).
>
>
Mathematica has pattern transforms as part of its language but its sequence
formula recognition commands are based on mathematical theories :

 - holonomic functions, linear algebra, z-transforms, difference equations,
continuous fractions, pade approximants, ...



> The system developed for that purpose is now available, both as a
> library/executable JAR (https://github.com/p-e-w/sequencer) and as a
> simple (beta stage) web service (http://www.sequenceboss.org/).
>
> At its core, Sequencer is a tree-based expression generator plus a
> hybrid search engine combining a fast numerical pre-checker with a
> symbolic verifier. Because the numerical checker is so fast, expressions
> of relatively high complexity (7-8 nodes) can be exhaustively searched
> in minutes on commodity hardware to check whether they generate the
> given numbers.
>
> Despite its early stage of development, Sequencer can already identify
> (i.e. find a closed form expression for) many sequences that OEIS,
> Superseeker and Mathematica can not. It is particularly strong at
> finding complex, nonlinear or inhomogeneous recurrence relations like
>
>   a(1) = 1
>   a(2) = 1
>   a(3) = 1
>   a(n) = a(n-2)^2+a(n-1)+a(n-3)   for n >= 4
>
> when provided the sequence
>
>   1, 1, 1, 3, 5, 15, 43, 273
>
> something which none of the above mentioned systems is currently able to
> do. But the system can also quickly find unusual, relatively simple
> general terms for sequences like
>
>   11, 47, 123, 214, 257
>
> for which Sequencer returns
>
>   a(n) = n + Binomial(10,n)
>
> in less than one second (http://www.sequenceboss.org/?q=11%2C+47%2C+123%
> 2C+214%2C+257).
>
> By leveraging the Symja computer algebra system, Sequencer supports
> fully symbolic input and output and is not limited to integer sequences.
> For example, running the program on the input
>
>   0, 1/2, sqrt(3)/2, 1
>
> produces (search depth 6) the formula
>
>   a(n) = Sin(1/6*Pi*(n-1))
>
>
> I invite you to give the Sequencer/SequenceBoss system a try. If you are
> familiar with Scala, you will find it easy to modify the
> FormulaGenerator class to expand the range of expressions that can be
> searched beyond what the command line switches already offer. Next in
> line I plan to add multicore support based on Scala Actors which should
> almost multiply the current search performance by the number of
> available CPU cores as the search is efficiently parallelizable. Bug
> reports and code contributions are very welcome, ideally on GitHub.
>
> Best regards
>
> Philipp Emanuel Weidmann
>


From wclark at mail.usf.edu  Mon Feb 23 17:02:37 2015
From: wclark at mail.usf.edu (W. Edwin Clark)
Date: Mon, 23 Feb 2015 11:02:37 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
Message-ID: <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>

On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <olivier.gerard at gmail.com>
wrote:

>
> It would be nice to test it on "hard" sequences and other sequences without
> formula.
>
>
>
For example:  http://oeis.org/A000001, the number of groups of order n :-)

Or perhaps easier:  http://oeis.org/A000688, the number of abelian groups
of order n.


From mlb at well.com  Mon Feb 23 22:02:26 2015
From: mlb at well.com (Marc LeBrun)
Date: Mon, 23 Feb 2015 13:02:26 -0800
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
Message-ID: <D110D562.19B0B%mlb@well.com>

It is my fond and enduring hope that the OEIS will someday enjoy the same
level of sophistication in its data science content as it does in its
mathematical content.

Features such as ad hoc keywords or categories are innocuous insofar as they
go, and useful within their scope, but they seem pretty primitive compared
to the current state-of-the-art in data modeling and knowledge engineering.

I recommend that anyone with an interest in these proposals with an eye
towards the future of the OEIS should look into things like the semantic web
to get a more up-to-date appreciation for where such technologies are going
(indeed, have already gone).

For example a keyword can be viewed as metadata that makes an assertion
*about a sequence*.  But instead of having "?" variants of every keyword one
can instead have a general kind of "meta" assertion *about an assertion*
that says it is conjectural.  And so on for many other applications (eg
assertions for provenance attribution, processing inferential consequences
of keywords such as prim==>nonn, etc etc).

The point is that there already exist sophisticated and elegant data
languages for representing this kind of information.  The OEIS should
consider adopting these approaches, rather than reinventing the wheel.

But heck, even if we just go ahead and kludge stuff up the good news is that
the total amount of actual data in the OEIS is truly miniscule by modern
standards.  This relative footprint will continue to shrink, at least while
the primary source of content continues to be entries hand-crafted by human
beings.  This means that building and maintaining useful informational
superstructures around the OEIS will lie well within the scope of
contemporary tools and techniques, and they can flourish off-site if not on.

With the current commercial interest around "big data" in many forms and its
consequent stimulation of academia, maybe we could get, say, a coven of grad
students to take a hands-on interest in this important aspect of the OEIS
and help us cook up something more au courant?




From mathar at mpia-hd.mpg.de  Mon Feb 23 23:21:39 2015
From: mathar at mpia-hd.mpg.de (Richard J. Mathar)
Date: Mon, 23 Feb 2015 23:21:39 +0100
Subject: [seqfan] Q on g.f. A138164
Message-ID: <20150223222139.GA13412@mathar.mpia-hd.mpg.de>

Is the generating function in http://oeis.org/A138164 correct?
The Maple implementation

vx := 2/sqrt(3)*sin(sin(x*3*sqrt(3)/2)/3) ;
A138164 := proc(n)
        1/(1-vx-vx^2) ;
        coeftayl(%,x=0,n) ;
end proc:
seq(%(n),n=0..13) ;

generates fractions from the power(x^3) on.


From pauldhanna at juno.com  Tue Feb 24 00:41:24 2015
From: pauldhanna at juno.com (Paul D Hanna)
Date: Mon, 23 Feb 2015 23:41:24 GMT
Subject: [seqfan] Re: Q on g.f. A138164
Message-ID: <20150223.184124.23772.0@webmail01.dca.untd.com>

Richard, 
     Good catch.  The formula should read: 
  
"G.f.: 1/(1-v-v^2) where v=(2/sqrt(3))*sin(arcsin(x*3*sqrt(3)/2)/3) is the series reversion of x*(1-x^2); ..."
 
(i.e., the second 'sin' should be 'arcsin') 
and a reference to A001764 would be in order since 
v = Sum_{n>=1} A001764(n-1)*x^(2*n-1). 
    Paul 
 
---------- Original Message ----------
From: "Richard J. Mathar" <mathar at mpia-hd.mpg.de>
To: seqfan at seqfan.eu
Subject: [seqfan] Q on g.f. A138164
Date: Mon, 23 Feb 2015 23:21:39 +0100

Is the generating function in http://oeis.org/A138164 correct?
The Maple implementation

vx := 2/sqrt(3)*sin(sin(x*3*sqrt(3)/2)/3) ;
A138164 := proc(n)
        1/(1-vx-vx^2) ;
        coeftayl(%,x=0,n) ;
end proc:
seq(%(n),n=0..13) ;

generates fractions from the power(x^3) on.

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/



From arndt at jjj.de  Tue Feb 24 08:56:40 2015
From: arndt at jjj.de (Joerg Arndt)
Date: Tue, 24 Feb 2015 08:56:40 +0100
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <D110D562.19B0B%mlb@well.com>
References: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <D110D562.19B0B%mlb@well.com>
Message-ID: <20150224075640.GA1671@jjj.de>

* Marc LeBrun <mlb at well.com> [Feb 24. 2015 08:40]:
> It is my fond and enduring hope that the OEIS will someday enjoy the same
> level of sophistication in its data science content as it does in its
> mathematical content.
> 
> [...]
> 
> With the current commercial interest around "big data" in many forms and its
> consequent stimulation of academia, maybe we could get, say, a coven of grad
> students to take a hands-on interest in this important aspect of the OEIS
> and help us cook up something more au courant?
> 
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/

I do agree with all you are saying.

There are plans for a "big data" project involving the OEIS, this is
related to the Zentralblatt-Math project that will hopefully start
soon-ish.  A student of mine is just finishing his thesis about parsing
formulas in the OEIS for the Zentralblatt.

Of course it all depends on the funding.

Best regards,  jj


From njasloane at gmail.com  Tue Feb 24 13:37:00 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 24 Feb 2015 07:37:00 -0500
Subject: [seqfan] Re: Additional keywords for OEIS
In-Reply-To: <20150224075640.GA1671@jjj.de>
References: <CAAOnSgRh1VhyyVkDZvbPiRzMBDXQXTRTymdgv1mLL=8x=3PZBA@mail.gmail.com>
 <D110D562.19B0B%mlb@well.com> <20150224075640.GA1671@jjj.de>
Message-ID: <CAAOnSgQV3o24CB4JDFCtjvuJw6zNY31RsU8ctypP867==yygUQ@mail.gmail.com>

> Of course it all depends on the funding.

If this becomes a problem, there is always the possibility that
the OEIS Foundation could try to raise some money to
help with the project.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Tue, Feb 24, 2015 at 2:56 AM, Joerg Arndt <arndt at jjj.de> wrote:

> * Marc LeBrun <mlb at well.com> [Feb 24. 2015 08:40]:
> > It is my fond and enduring hope that the OEIS will someday enjoy the same
> > level of sophistication in its data science content as it does in its
> > mathematical content.
> >
> > [...]
> >
> > With the current commercial interest around "big data" in many forms and
> its
> > consequent stimulation of academia, maybe we could get, say, a coven of
> grad
> > students to take a hands-on interest in this important aspect of the OEIS
> > and help us cook up something more au courant?
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> I do agree with all you are saying.
>
> There are plans for a "big data" project involving the OEIS, this is
> related to the Zentralblatt-Math project that will hopefully start
> soon-ish.  A student of mine is just finishing his thesis about parsing
> formulas in the OEIS for the Zentralblatt.
>
> Of course it all depends on the funding.
>
> Best regards,  jj
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From reddwarf2956 at yahoo.com  Mon Feb 23 05:04:01 2015
From: reddwarf2956 at yahoo.com (John W. Nicholson)
Date: Mon, 23 Feb 2015 04:04:01 +0000 (UTC)
Subject: [seqfan] Re: Is there any problems with this proof?
In-Reply-To: <CAE3sB-CuevC0dyw7c-uut2NVDBdbCuKRj2uyS74GdST0uR=MVw@mail.gmail.com>
References: <CAE3sB-CuevC0dyw7c-uut2NVDBdbCuKRj2uyS74GdST0uR=MVw@mail.gmail.com>
Message-ID: <370292300.7299941.1424664241563.JavaMail.yahoo@mail.yahoo.com>

Alexei Kourbatov,
First of all thanks for being clear with your concerns. Second, do remember the note:

"All gaps g_i = p_{i+1} ? p_i, where p_i < p_y are g_i <= G_n(x)."

Maybe I need to add the following:

Under the assumption that the smaller gap is p_{y-b+1} - p_{y-b} = G_n(x), we see that the larger gap is p_{y+1} - p_y <= 2*G_n(x).

Is that OK??John W. Nicholson 

     On Sunday, February 22, 2015 5:17 PM, Alexei Kourbatov <akourbatov at gmail.com> wrote:
   
 

 In Cramer's model, I feel that both statements are true with probability 1.

In the original proof, the last sentence "So the gap g_y ..." apparently
does not follow from the preceding statements (as far as I can tell).
To illustrate my point: a-c < 2(b-d) does not follow from { a < 2b and c <
2d} - but it would follow e.g. from { a < 2b and c >= 2d}



On Sat, Feb 21, 2015 at 7:42 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> I don't know what to think of the first question. It's numerically
> unassailable -- to build up evidence in the primes, one way or another,
> you'd probably need to get a lot closer to a googolplex than a googol, and
> even 10^20 is out of reach at the moment. The only recourse I see is
> checking whether it holds in the Cramer model, flawed as it is.
>
> It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
> also wouldn't surprise me if it happened only finitely often.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Charles,
> >
> > Does that mean that the proof with first question, that the ratio <=2, is
> > correct and with out problems so that you are now looking at the second
> > question with the limit of the ratio going to infinity =1? John W.
> Nicholson
> >
> >? ? ? On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> > charles.greathouse at case.edu> wrote:
> >
> >
> >
> >? I suspect that there is some k > 1 such that the ratio is greater than k
> > infinitely often. Is anyone interested in crunching the numbers here on
> the
> > heuristic?
> >
> > Charles Greathouse
> > Analyst/Programmer
> > Case Western Reserve University
> >
> > On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <
> reddwarf2956 at yahoo.com
> > >
> > wrote:
> >
> > > Below is a proof based on A005250(n ) of the OEIS.? Can someone look at
> > it
> > > and tell me if it true?
> > >
> > >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > > If it is true, an edit of A005250 comments is needed.
> > >
> > > Related:
> > >
> > >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> > >
> > >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> > >
> > >
> > >? John W. Nicholson
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


 
   


From pew at worldwidemann.com  Mon Feb 23 19:21:07 2015
From: pew at worldwidemann.com (Philipp Emanuel Weidmann)
Date: Mon, 23 Feb 2015 19:21:07 +0100
Subject: [seqfan]  Re: Purely algorithmic number sequence identification
In-Reply-To: <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
Message-ID: <1424715667.2631.30.camel@worldwidemann.com>

Well, it turns out the first eight elements of A000001 satisfy the, umm,
"slightly exotic" recurrence relation

  a(1) = 1
  a(2) = 1
  a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3

;)

In earnest, while I doubt that brute forcing formulas will bring any
insight into sequences that have baffled mathematicians for centuries
with their irregularity, what might indeed be interesting is to run the
system not on one sequence, but on tens of thousands, all of which have
no closed-form expression associated with them (is there a way to query
those on OEIS?). In a matter of days, Sequencer would likely return a
hundred or so closed forms, some of which may prove correct, which could
then be investigated rigorously.

For such a search, I should probably also add a lot more combinatorial
and number theoretic primitives to the formula generator ? whenever I
randomly browse around OEIS, most of the sequences seem to be counting
problems of some kind.

Best regards
Philipp




On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <olivier.gerard at gmail.com>
> wrote:
> 
> >
> > It would be nice to test it on "hard" sequences and other sequences without
> > formula.
> >
> >
> >
> For example:  http://oeis.org/A000001, the number of groups of order n :-)
> 
> Or perhaps easier:  http://oeis.org/A000688, the number of abelian groups
> of order n.
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/




From njasloane at gmail.com  Tue Feb 24 14:17:28 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Tue, 24 Feb 2015 08:17:28 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <1424715667.2631.30.camel@worldwidemann.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
Message-ID: <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>

What do you think of adding your program to Superseeker?  It sounds like
this would definitely be worth doing.

By the way, can you do anything with A122536?  We have 200 terms, but no
formula or recurrence!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
pew at worldwidemann.com> wrote:

> Well, it turns out the first eight elements of A000001 satisfy the, umm,
> "slightly exotic" recurrence relation
>
>   a(1) = 1
>   a(2) = 1
>   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>
> ;)
>
> In earnest, while I doubt that brute forcing formulas will bring any
> insight into sequences that have baffled mathematicians for centuries
> with their irregularity, what might indeed be interesting is to run the
> system not on one sequence, but on tens of thousands, all of which have
> no closed-form expression associated with them (is there a way to query
> those on OEIS?). In a matter of days, Sequencer would likely return a
> hundred or so closed forms, some of which may prove correct, which could
> then be investigated rigorously.
>
> For such a search, I should probably also add a lot more combinatorial
> and number theoretic primitives to the formula generator ? whenever I
> randomly browse around OEIS, most of the sequences seem to be counting
> problems of some kind.
>
> Best regards
> Philipp
>
>
>
>
> On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
> olivier.gerard at gmail.com>
> > wrote:
> >
> > >
> > > It would be nice to test it on "hard" sequences and other sequences
> without
> > > formula.
> > >
> > >
> > >
> > For example:  http://oeis.org/A000001, the number of groups of order n
> :-)
> >
> > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
> groups
> > of order n.
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From benoit.jubin at gmail.com  Tue Feb 24 17:49:38 2015
From: benoit.jubin at gmail.com (=?UTF-8?Q?Beno=C3=AEt_Jubin?=)
Date: Tue, 24 Feb 2015 17:49:38 +0100
Subject: [seqfan] Improved lower bound for A250000
Message-ID: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>

Dear seqfans,

Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on
an (n,n) chessboard.

By modifying the Pratt--Selcoe configuration, I improved the best known
lower bound from
a(n) > (9/4)*(n/4)^2
to
a(n) > (7/3)*(n/4)^2.
I have been sloppy with side effects, but to be on the safe side, let's say
a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the
coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the
following description.

The configuration in the limit n = infinity is as follows: denoting by x,y
in [0,1] the coordinates on the chessboard, the queens of one color are in
the two regions
x<1/4, y<1/2, x<y<x+1/3
and
1/2<x<3/4, y<x-1/3, y<1-x
and the queens of the other color are obtained by central symmetry. As you
can guess, I obtained these coefficients by equalizing the lengths of the
"opposite" boundaries of the armies (this already improves (by 1) on the
"Board 4" example of the webpage).

Using an easy upper bound, one has asymptotically
(2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
Anyone to help fill the gap?

Best,
Benoit


From Rob.Pratt at sas.com  Tue Feb 24 18:13:26 2015
From: Rob.Pratt at sas.com (Rob Pratt)
Date: Tue, 24 Feb 2015 17:13:26 +0000
Subject: [seqfan] Re: Improved lower bound for A250000
In-Reply-To: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
References: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
Message-ID: <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>

Please share your n =24 solution.  Under the central symmetry constraint, I get a maximum of 80, not 84.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Beno?t Jubin
Sent: Tuesday, February 24, 2015 11:50 AM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Improved lower bound for A250000

Dear seqfans,

Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on an (n,n) chessboard.

By modifying the Pratt--Selcoe configuration, I improved the best known lower bound from
a(n) > (9/4)*(n/4)^2
to
a(n) > (7/3)*(n/4)^2.
I have been sloppy with side effects, but to be on the safe side, let's say
a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the following description.

The configuration in the limit n = infinity is as follows: denoting by x,y in [0,1] the coordinates on the chessboard, the queens of one color are in the two regions x<1/4, y<1/2, x<y<x+1/3 and 1/2<x<3/4, y<x-1/3, y<1-x and the queens of the other color are obtained by central symmetry. As you can guess, I obtained these coefficients by equalizing the lengths of the "opposite" boundaries of the armies (this already improves (by 1) on the "Board 4" example of the webpage).

Using an easy upper bound, one has asymptotically
(2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
Anyone to help fill the gap?

Best,
Benoit

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/

From benoit.jubin at gmail.com  Tue Feb 24 18:25:19 2015
From: benoit.jubin at gmail.com (=?UTF-8?Q?Beno=C3=AEt_Jubin?=)
Date: Tue, 24 Feb 2015 18:25:19 +0100
Subject: [seqfan] Re: Improved lower bound for A250000
In-Reply-To: <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>
References: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
 <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>
Message-ID: <CAEG8PYvDamRCbDj9dfC=cyeLrpYLThJGPZyCqr6QMvvt_wEKUQ@mail.gmail.com>

Dear Rob,
I improved by one the final board on the webpage by using the same idea as
for my asymptotic bound, but you are right that in this specific case, the
result is not centrally symmetric. From the last example on the webpage, I
made marginal changes along the diagonals (in the [0,1]^2 coordinates)
y=x+1/3 (deleted 3 Ws, added 5 Bs) and y=x-1/3 (deleted 4 Bs, added 4Ws):

------------------------

......WWWWWW............

......WWWWWW...........W

......WWWWWW..........WW

......WWWWWW.........WWW

......WWWWWW........WWWW

......WWWWW........WWWWW

.......WWW........WWWWWW

........W.........WWWWWW

..................WWWWWW

..................WWWWW.

..................WWWW..

..................WWW...

....BB..................

...BBB..................

..BBBB..................

.BBBBB..................

BBBBBB..........B.......

BBBBBB.........BBB......

BBBBBB........BBBB......

BBBBB........BBBBB......

BBBB........BBBBBB......

BBB.........BBBBBB......

BB..........BBBBBB......

B...........BBBBBB......

------------------------



On Tue, Feb 24, 2015 at 6:13 PM, Rob Pratt <Rob.Pratt at sas.com> wrote:

> Please share your n =24 solution.  Under the central symmetry constraint,
> I get a maximum of 80, not 84.
>
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Beno?t
> Jubin
> Sent: Tuesday, February 24, 2015 11:50 AM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Improved lower bound for A250000
>
> Dear seqfans,
>
> Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on
> an (n,n) chessboard.
>
> By modifying the Pratt--Selcoe configuration, I improved the best known
> lower bound from
> a(n) > (9/4)*(n/4)^2
> to
> a(n) > (7/3)*(n/4)^2.
> I have been sloppy with side effects, but to be on the safe side, let's say
> a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the
> coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the
> following description.
>
> The configuration in the limit n = infinity is as follows: denoting by x,y
> in [0,1] the coordinates on the chessboard, the queens of one color are in
> the two regions x<1/4, y<1/2, x<y<x+1/3 and 1/2<x<3/4, y<x-1/3, y<1-x and
> the queens of the other color are obtained by central symmetry. As you can
> guess, I obtained these coefficients by equalizing the lengths of the
> "opposite" boundaries of the armies (this already improves (by 1) on the
> "Board 4" example of the webpage).
>
> Using an easy upper bound, one has asymptotically
> (2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
> Anyone to help fill the gap?
>
> Best,
> Benoit
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From Eric.Angelini at kntv.be  Tue Feb 24 19:13:22 2015
From: Eric.Angelini at kntv.be (Eric Angelini)
Date: Tue, 24 Feb 2015 19:13:22 +0100
Subject: [seqfan] Prime by concatenation
Message-ID: <8B00BFBA136BAB43AD27F9EDC3758F03BD24CA5286@KNTVSRV01.kntv.local>

Hello Seqfans,
Concatenate any two digits of S separated by a comma: 
the resulting 2-digit number is prime.

If we accept that [70,2] produces the prime "2"
(concatenation of 0 and 2), then S is a permutation
of {the positive integers} - {4,6,8,9}:

S = 1,3,7,9,70,2,30,5,31,10,20,21,11,12,32,33,13,14,15,...

As usual, S was extended with the smallest integer
not yet present in S and not leading to a contradiction.

Best,
?.






From pew at worldwidemann.com  Tue Feb 24 21:37:36 2015
From: pew at worldwidemann.com (Philipp Emanuel Weidmann)
Date: Tue, 24 Feb 2015 21:37:36 +0100
Subject: [seqfan]  Re: Purely algorithmic number sequence identification
In-Reply-To: <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
 <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
Message-ID: <1424810256.2771.27.camel@worldwidemann.com>

Sounds good, how would that work? Sequencer already has a public API
(documented at https://github.com/p-e-w/sequencer#api) so integration
should be easy as long as Superseeker has a way to interface with a JVM
library.

As for A122536, nothing so far I'm afraid. I really would like to run a
mass search on sequences without formulas though. Do you perhaps know of
a way to find just those on OEIS? Soon the batch of performance
improvements I'm currently working on will be finished, and then
Sequencer should be able to search all depth 6 formulas for more than
1000 Sequences per day. Also, a batch mode could be implemented, which
would allow the program to process a large number of sequences at once,
dramatically improving performance for this use case. Indeed, all of
OEIS could be checked this way in about a week probably ? which would
also be interesting for sequences that already *have* formulas, as some
of them may possess interesting alternative forms, or be incorrect.

Best regards
Philipp





On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
> What do you think of adding your program to Superseeker?  It sounds like
> this would definitely be worth doing.
> 
> By the way, can you do anything with A122536?  We have 200 terms, but no
> formula or recurrence!
> 
> Best regards
> Neil
> 
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
> 
> 
> On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
> pew at worldwidemann.com> wrote:
> 
> > Well, it turns out the first eight elements of A000001 satisfy the, umm,
> > "slightly exotic" recurrence relation
> >
> >   a(1) = 1
> >   a(2) = 1
> >   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
> >
> > ;)
> >
> > In earnest, while I doubt that brute forcing formulas will bring any
> > insight into sequences that have baffled mathematicians for centuries
> > with their irregularity, what might indeed be interesting is to run the
> > system not on one sequence, but on tens of thousands, all of which have
> > no closed-form expression associated with them (is there a way to query
> > those on OEIS?). In a matter of days, Sequencer would likely return a
> > hundred or so closed forms, some of which may prove correct, which could
> > then be investigated rigorously.
> >
> > For such a search, I should probably also add a lot more combinatorial
> > and number theoretic primitives to the formula generator ? whenever I
> > randomly browse around OEIS, most of the sequences seem to be counting
> > problems of some kind.
> >
> > Best regards
> > Philipp
> >
> >
> >
> >
> > On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> > > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
> > olivier.gerard at gmail.com>
> > > wrote:
> > >
> > > >
> > > > It would be nice to test it on "hard" sequences and other sequences
> > without
> > > > formula.
> > > >
> > > >
> > > >
> > > For example:  http://oeis.org/A000001, the number of groups of order n
> > :-)
> > >
> > > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
> > groups
> > > of order n.
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/




From franktaw at netscape.net  Wed Feb 25 00:17:03 2015
From: franktaw at netscape.net (Frank Adams-Watters)
Date: Tue, 24 Feb 2015 18:17:03 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <1424810256.2771.27.camel@worldwidemann.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
 <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
 <1424810256.2771.27.camel@worldwidemann.com>
Message-ID: <8D21E9F22268966-720-A8A7C@webmail-vm046.sysops.aol.com>

If you search in the native format for sequences without "%F" lines, 
you will find the sequences with no formulas present at all. This still 
leaves a larger number of sequences for which some formula has been 
added, but not a formula specifically to define the sequence.

Franklin T. Adams-Watters

-----Original Message-----
From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
To: seqfan <seqfan at list.seqfan.eu>
Sent: Tue, Feb 24, 2015 5:09 pm
Subject: [seqfan]  Re: Purely algorithmic number sequence identification


Sounds good, how would that work? Sequencer already has a public API
(documented at https://github.com/p-e-w/sequencer#api) so integration
should be easy as long as Superseeker has a way to interface with a JVM
library.

As for A122536, nothing so far I'm afraid. I really would like to run a
mass search on sequences without formulas though. Do you perhaps know of
a way to find just those on OEIS? Soon the batch of performance
improvements I'm currently working on will be finished, and then
Sequencer should be able to search all depth 6 formulas for more than
1000 Sequences per day. Also, a batch mode could be implemented, which
would allow the program to process a large number of sequences at once,
dramatically improving performance for this use case. Indeed, all of
OEIS could be checked this way in about a week probably ? which would
also be interesting for sequences that already *have* formulas, as some
of them may possess interesting alternative forms, or be incorrect.

Best regards
Philipp





On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
> What do you think of adding your program to Superseeker?  It sounds 
like
> this would definitely be worth doing.
>
> By the way, can you do anything with A122536?  We have 200 terms, but 
no
> formula or recurrence!
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, 
NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
> pew at worldwidemann.com> wrote:
>
> > Well, it turns out the first eight elements of A000001 satisfy the, 
umm,
> > "slightly exotic" recurrence relation
> >
> >   a(1) = 1
> >   a(2) = 1
> >   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
> >
> > ;)
> >
> > In earnest, while I doubt that brute forcing formulas will bring any
> > insight into sequences that have baffled mathematicians for 
centuries
> > with their irregularity, what might indeed be interesting is to run 
the
> > system not on one sequence, but on tens of thousands, all of which 
have
> > no closed-form expression associated with them (is there a way to 
query
> > those on OEIS?). In a matter of days, Sequencer would likely return 
a
> > hundred or so closed forms, some of which may prove correct, which 
could
> > then be investigated rigorously.
> >
> > For such a search, I should probably also add a lot more 
combinatorial
> > and number theoretic primitives to the formula generator ? whenever 
I
> > randomly browse around OEIS, most of the sequences seem to be 
counting
> > problems of some kind.
> >
> > Best regards
> > Philipp
> >
> >
> >
> >
> > On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> > > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
> > olivier.gerard at gmail.com>
> > > wrote:
> > >
> > > >
> > > > It would be nice to test it on "hard" sequences and other 
sequences
> > without
> > > > formula.
> > > >
> > > >
> > > >
> > > For example:  http://oeis.org/A000001, the number of groups of 
order n
> > :-)
> > >
> > > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
> > groups
> > > of order n.
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/



_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/


  


From 2stepan at rambler.ru  Tue Feb 24 21:41:21 2015
From: 2stepan at rambler.ru (=?koi8-r?B?wNLJyiDHxdLB08nNz9c=?=)
Date: Tue, 24 Feb 2015 23:41:21 +0300
Subject: [seqfan] magma calculator
In-Reply-To: <1424810477.253256.19611.44231@mail.rambler.ru>
References: <1424810477.253256.19611.44231@mail.rambler.ru>
Message-ID: <1424810481.1426.15492.48037@mail.rambler.ru>


Dear SeqFans. 

Magma calculator: a(27) = ? and a(64) = ? if  a(n) = smallest k such that k^n + n is prime: 

1, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 417, 2, 1, 0, 1, 0, 81, 

76, 1, 0, 55, 28, 15, (a(27) = ?), 1, 0, 1, 0, 117, 230, 3, 12, 1, 0, 375, 2, 1, 

0, 1, 0, 25, 218, 1, 0, 7, 100, 993, 28, 1, 0, 13, 252, 183, 226, 1, 0, 1, 

0, 777, 1294, (a(64) = ?), 1806, ...

Thanks, JSG

From olivier.gerard at gmail.com  Wed Feb 25 00:26:31 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Wed, 25 Feb 2015 00:26:31 +0100
Subject: [seqfan] Re: magma calculator
In-Reply-To: <1424810481.1426.15492.48037@mail.rambler.ru>
References: <1424810477.253256.19611.44231@mail.rambler.ru>
 <1424810481.1426.15492.48037@mail.rambler.ru>
Message-ID: <CAAcpPSaO6bZFt_T9TU9HtBxUC4mv9O7dPzDA7Ta8sqU7yPNtAw@mail.gmail.com>

Dear Youri,

If you are on seqfan, why don't use the OEIS first to gain more knowledge ?

Look at http://oeis.org/A072883

and you will have the explanation why a(27) and a(64) have no solutions.

A good rule to lookup something in the OEIS is : never assume that your
own conventions about initial terms, offset, meaning of 0 and 1 have been
chosen
by everyone.



Olivier

PS: please next time, find a more appropriate title for your mail. What you
are discussing
is not the magma calculator but a particular computation you did with it.






On Tue, Feb 24, 2015 at 9:41 PM, ???? ????????? <2stepan at rambler.ru> wrote:

>
> Dear SeqFans.
> Magma calculator: a(27) = ? and a(64) = ? if  a(n) = smallest k such that
> k^n + n is prime:
> 1, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 417, 2, 1, 0, 1, 0, 81,
> 76, 1, 0, 55, 28, 15, (a(27) = ?), 1, 0, 1, 0, 117, 230, 3, 12, 1, 0, 375,
> 2, 1,
> 0, 1, 0, 25, 218, 1, 0, 7, 100, 993, 28, 1, 0, 13, 252, 183, 226, 1, 0, 1,
> 0, 777, 1294, (a(64) = ?), 1806, ...
>
> Thanks, JSG
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From israel at math.ubc.ca  Wed Feb 25 00:30:45 2015
From: israel at math.ubc.ca (israel at math.ubc.ca)
Date: 24 Feb 2015 15:30:45 -0800
Subject: [seqfan] Re: magma calculator
In-Reply-To: <1424810481.1426.15492.48037@mail.rambler.ru>
References: <1424810477.253256.19611.44231@mail.rambler.ru>
 <1424810481.1426.15492.48037@mail.rambler.ru>
Message-ID: <Prayer.1.3.5.1502241530450.7384@viol.math.ubc.ca>


x^27 + 27 is divisible by x^9 + 3, x^64 + 64 is divisible by x^32-4*x^16+8.

Cheers,
Robert

On Feb 24 2015, ???? ????????? wrote:

>
>Dear SeqFans. 
>
> Magma calculator: a(27) = ? and a(64) = ? if a(n) = smallest k such that 
> k^n + n is prime:
>
>1, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 417, 2, 1, 0, 1, 0, 81, 
>
> 76, 1, 0, 55, 28, 15, (a(27) = ?), 1, 0, 1, 0, 117, 230, 3, 12, 1, 0, 
> 375, 2, 1,
>
>0, 1, 0, 25, 218, 1, 0, 7, 100, 993, 28, 1, 0, 13, 252, 183, 226, 1, 0, 1, 
>
>0, 777, 1294, (a(64) = ?), 1806, ...
>
>Thanks, JSG
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>


From charles.greathouse at case.edu  Wed Feb 25 07:34:47 2015
From: charles.greathouse at case.edu (Charles Greathouse)
Date: Wed, 25 Feb 2015 01:34:47 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <1424810256.2771.27.camel@worldwidemann.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
 <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
 <1424810256.2771.27.camel@worldwidemann.com>
Message-ID: <CAAkfSGLZzqWEQ5xQiGgBBwh2mQzJXZ9sandhyO4-aovytL=WiQ@mail.gmail.com>

There are about 100,000 sequences with %F lines and about 150,000 without.
It's probably worthwhile to run it on all the sequences in
oeis.org/stripped.gz.

I think adding the Sequencer to the Superseeker would be great -- at least
through depth 5, which takes a second or two, and possibly to depth 6
depending on our free processor time (in my experiments this takes a few
minutes). I imagine the easiest way would be to run it as a black box,
dumping the result to a temp file?

Yangchen Pan and Max Alekseyev were working on a project looking for
relations between OEIS sequences, they may also have useful information.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Tue, Feb 24, 2015 at 3:37 PM, Philipp Emanuel Weidmann <
pew at worldwidemann.com> wrote:

> Sounds good, how would that work? Sequencer already has a public API
> (documented at https://github.com/p-e-w/sequencer#api) so integration
> should be easy as long as Superseeker has a way to interface with a JVM
> library.
>
> As for A122536, nothing so far I'm afraid. I really would like to run a
> mass search on sequences without formulas though. Do you perhaps know of
> a way to find just those on OEIS? Soon the batch of performance
> improvements I'm currently working on will be finished, and then
> Sequencer should be able to search all depth 6 formulas for more than
> 1000 Sequences per day. Also, a batch mode could be implemented, which
> would allow the program to process a large number of sequences at once,
> dramatically improving performance for this use case. Indeed, all of
> OEIS could be checked this way in about a week probably ? which would
> also be interesting for sequences that already *have* formulas, as some
> of them may possess interesting alternative forms, or be incorrect.
>
> Best regards
> Philipp
>
>
>
>
>
> On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
> > What do you think of adding your program to Superseeker?  It sounds like
> > this would definitely be worth doing.
> >
> > By the way, can you do anything with A122536?  We have 200 terms, but no
> > formula or recurrence!
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
> >
> > On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
> > pew at worldwidemann.com> wrote:
> >
> > > Well, it turns out the first eight elements of A000001 satisfy the,
> umm,
> > > "slightly exotic" recurrence relation
> > >
> > >   a(1) = 1
> > >   a(2) = 1
> > >   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
> > >
> > > ;)
> > >
> > > In earnest, while I doubt that brute forcing formulas will bring any
> > > insight into sequences that have baffled mathematicians for centuries
> > > with their irregularity, what might indeed be interesting is to run the
> > > system not on one sequence, but on tens of thousands, all of which have
> > > no closed-form expression associated with them (is there a way to query
> > > those on OEIS?). In a matter of days, Sequencer would likely return a
> > > hundred or so closed forms, some of which may prove correct, which
> could
> > > then be investigated rigorously.
> > >
> > > For such a search, I should probably also add a lot more combinatorial
> > > and number theoretic primitives to the formula generator ? whenever I
> > > randomly browse around OEIS, most of the sequences seem to be counting
> > > problems of some kind.
> > >
> > > Best regards
> > > Philipp
> > >
> > >
> > >
> > >
> > > On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> > > > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
> > > olivier.gerard at gmail.com>
> > > > wrote:
> > > >
> > > > >
> > > > > It would be nice to test it on "hard" sequences and other sequences
> > > without
> > > > > formula.
> > > > >
> > > > >
> > > > >
> > > > For example:  http://oeis.org/A000001, the number of groups of
> order n
> > > :-)
> > > >
> > > > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
> > > groups
> > > > of order n.
> > > >
> > > > _______________________________________________
> > > >
> > > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From antti.karttunen at gmail.com  Wed Feb 25 09:12:54 2015
From: antti.karttunen at gmail.com (Antti Karttunen)
Date: Wed, 25 Feb 2015 10:12:54 +0200
Subject: [seqfan] Re: Purely algorithmic number sequence identification
Message-ID: <CAB+0_=nG2LrDnSvMZnBCuQY3A53vJacH-PKdkCrjkP2vrc6OUw@mail.gmail.com>

On Tue, Feb 24, 2015 at 3:06 PM,  <seqfan-request at list.seqfan.eu> wrote:

> Message: 12
> Date: Mon, 23 Feb 2015 19:21:07 +0100
> From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
> To: seqfan at list.seqfan.eu
> Subject: [seqfan]  Re: Purely algorithmic number sequence
>         identification
> Message-ID: <1424715667.2631.30.camel at worldwidemann.com>
> Content-Type: text/plain; charset="UTF-8"
>
> Well, it turns out the first eight elements of A000001 satisfy the, umm,
> "slightly exotic" recurrence relation
>
>   a(1) = 1
>   a(2) = 1
>   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>
> ;)
>
> In earnest, while I doubt that brute forcing formulas will bring any
> insight into sequences that have baffled mathematicians for centuries
> with their irregularity, what might indeed be interesting is to run the
> system not on one sequence, but on tens of thousands, all of which have
> no closed-form expression associated with them (is there a way to query
> those on OEIS?). In a matter of days, Sequencer would likely return a
> hundred or so closed forms, some of which may prove correct, which could
> then be investigated rigorously.
>
> For such a search, I should probably also add a lot more combinatorial
> and number theoretic primitives to the formula generator ? whenever I
> randomly browse around OEIS, most of the sequences seem to be counting
> problems of some kind.

Kudos for interesting development!

Yes, especially number theoretic primitives would be welcome, because
for now your system does not exactly shine on any such sequences. For
example, although it correctly identifies factorials:

http://www.sequenceboss.org/?q=1%2C2%2C6%2C24%2C120%2C720%2C5040

then for primorials https://oeis.org/A002110 it remains baffled:
http://www.sequenceboss.org/?q=1%2C+2%2C+6%2C+30%2C+210%2C+2310%2C+30030%2C+510510%2C+9699690

Neither any success with the squares of primes:
http://www.sequenceboss.org/?q=4%2C+9%2C+25%2C+49%2C+121%2C+169%2C+289

(Not to speak about any of A000005, A000010 or A000203).

Now, when testing the third row of "Ludic array"
https://oeis.org/A255127

http://www.sequenceboss.org/?q=5%2C+19%2C+35%2C+49%2C+65%2C+79%2C+95%2C+109%2C+125%2C+139%2C+155%2C+169

the SequenceBoss, guesses a working recurrence for it:

a_1 = 5, a_2 = 19, a3 = 35, a_n = a_{n-2} - a_{n-3} + a_{n-1} for n >= 4

(This mirrors the recurrence a(n) = a(n-1) + a(n-2) - a(n-3), n>=4
given for A007310 by Roger Bagula)


No such success with the later rows of A255127 though:

http://www.sequenceboss.org/?q=7%2C+31%2C+59%2C+85%2C+113%2C+137%2C+163%2C+191%2C+217%2C+241

http://www.sequenceboss.org/?q=11%2C++55%2C+103%2C+151%2C+203%2C+251%2C++299%2C++343%2C++391%2C++443

(although when looking at their graphs, they all look awfully linear...)


Cheers,

Antti

>
> Best regards
> Philipp
>


From antti.karttunen at gmail.com  Wed Feb 25 10:24:23 2015
From: antti.karttunen at gmail.com (Antti Karttunen)
Date: Wed, 25 Feb 2015 11:24:23 +0200
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <CAB+0_=nG2LrDnSvMZnBCuQY3A53vJacH-PKdkCrjkP2vrc6OUw@mail.gmail.com>
References: <CAB+0_=nG2LrDnSvMZnBCuQY3A53vJacH-PKdkCrjkP2vrc6OUw@mail.gmail.com>
Message-ID: <CAB+0_=nbQGvf_PX3HdGK0hB6TkJXL1_tsxurCtydeZ+G1fyCtQ@mail.gmail.com>

Neither any success with A000265
http://www.sequenceboss.org/?q=1%2C+1%2C+3%2C+1%2C+5%2C+3%2C+7%2C+1%2C+9%2C+5%2C+11%2C+3%2C+13%2C+7%2C+15%2C+1%2C+17
(or the associated A003602)

Nor with sequences like:
https://oeis.org/A126760
or:
https://oeis.org/A254104
(nor its inverse A254103).


These kinds of sequences are very common in OEIS, where one doesn't
recurse with some constant offset decremented from n (as in a(n-1) +
a(n-2)) but with n/2 (if n is even) and say, with (n-1)/2 if n is odd.

Maybe also some "p-adic primitives" would be good, e.g. applying A007814 ?


Best,

Antti


On Wed, Feb 25, 2015 at 10:12 AM, Antti Karttunen
<antti.karttunen at gmail.com> wrote:
> On Tue, Feb 24, 2015 at 3:06 PM,  <seqfan-request at list.seqfan.eu> wrote:
>
>> Message: 12
>> Date: Mon, 23 Feb 2015 19:21:07 +0100
>> From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
>> To: seqfan at list.seqfan.eu
>> Subject: [seqfan]  Re: Purely algorithmic number sequence
>>         identification
>> Message-ID: <1424715667.2631.30.camel at worldwidemann.com>
>> Content-Type: text/plain; charset="UTF-8"
>>
>> Well, it turns out the first eight elements of A000001 satisfy the, umm,
>> "slightly exotic" recurrence relation
>>
>>   a(1) = 1
>>   a(2) = 1
>>   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>>
>> ;)
>>
>> In earnest, while I doubt that brute forcing formulas will bring any
>> insight into sequences that have baffled mathematicians for centuries
>> with their irregularity, what might indeed be interesting is to run the
>> system not on one sequence, but on tens of thousands, all of which have
>> no closed-form expression associated with them (is there a way to query
>> those on OEIS?). In a matter of days, Sequencer would likely return a
>> hundred or so closed forms, some of which may prove correct, which could
>> then be investigated rigorously.
>>
>> For such a search, I should probably also add a lot more combinatorial
>> and number theoretic primitives to the formula generator ? whenever I
>> randomly browse around OEIS, most of the sequences seem to be counting
>> problems of some kind.
>
> Kudos for interesting development!
>
> Yes, especially number theoretic primitives would be welcome, because
> for now your system does not exactly shine on any such sequences. For
> example, although it correctly identifies factorials:
>
> http://www.sequenceboss.org/?q=1%2C2%2C6%2C24%2C120%2C720%2C5040
>
> then for primorials https://oeis.org/A002110 it remains baffled:
> http://www.sequenceboss.org/?q=1%2C+2%2C+6%2C+30%2C+210%2C+2310%2C+30030%2C+510510%2C+9699690
>
> Neither any success with the squares of primes:
> http://www.sequenceboss.org/?q=4%2C+9%2C+25%2C+49%2C+121%2C+169%2C+289
>
> (Not to speak about any of A000005, A000010 or A000203).
>
> Now, when testing the third row of "Ludic array"
> https://oeis.org/A255127
>
> http://www.sequenceboss.org/?q=5%2C+19%2C+35%2C+49%2C+65%2C+79%2C+95%2C+109%2C+125%2C+139%2C+155%2C+169
>
> the SequenceBoss, guesses a working recurrence for it:
>
> a_1 = 5, a_2 = 19, a3 = 35, a_n = a_{n-2} - a_{n-3} + a_{n-1} for n >= 4
>
> (This mirrors the recurrence a(n) = a(n-1) + a(n-2) - a(n-3), n>=4
> given for A007310 by Roger Bagula)
>
>
> No such success with the later rows of A255127 though:
>
> http://www.sequenceboss.org/?q=7%2C+31%2C+59%2C+85%2C+113%2C+137%2C+163%2C+191%2C+217%2C+241
>
> http://www.sequenceboss.org/?q=11%2C++55%2C+103%2C+151%2C+203%2C+251%2C++299%2C++343%2C++391%2C++443
>
> (although when looking at their graphs, they all look awfully linear...)
>
>
> Cheers,
>
> Antti
>
>>
>> Best regards
>> Philipp
>>


From apovolot at gmail.com  Wed Feb 25 01:32:49 2015
From: apovolot at gmail.com (apovolot at gmail.com)
Date: Tue, 24 Feb 2015 19:32:49 -0500
Subject: [seqfan] Re: Purely algorithmic number sequence identification
In-Reply-To: <8D21E9F22268966-720-A8A7C@webmail-vm046.sysops.aol.com>
References: <1424640557.3507.31.camel@worldwidemann.com>
 <CAAcpPSa+m0UbkhVb=qbraqxOacqOa-DwqeNMHLJZ_9tuHoz6iw@mail.gmail.com>
 <CABOJUO6C=szKmf6UZ0pABkZpNcSJKw22uxbAnaGCaH=-qz8zqg@mail.gmail.com>
 <1424715667.2631.30.camel@worldwidemann.com>
 <CAAOnSgT9CypwD5+u7iLFEx97ALJvUWzhquqZKwhuUxXeQD0yyg@mail.gmail.com>
 <1424810256.2771.27.camel@worldwidemann.com>
 <8D21E9F22268966-720-A8A7C@webmail-vm046.sysops.aol.com>
Message-ID: <243EA8F9-2612-43D6-AFAF-2E42A32F53CA@gmail.com>

Could usage of the prefix
formula: 
be somehow employed to the sequences with no formulas present at all ?

> On Feb 24, 2015, at 6:17 PM, Frank Adams-Watters <franktaw at netscape.net> wrote:
> 
> If you search in the native format for sequences without "%F" lines, you will find the sequences with no formulas present at all. This still leaves a larger number of sequences for which some formula has been added, but not a formula specifically to define the sequence.
> 
> Franklin T. Adams-Watters
> 
> -----Original Message-----
> From: Philipp Emanuel Weidmann <pew at worldwidemann.com>
> To: seqfan <seqfan at list.seqfan.eu>
> Sent: Tue, Feb 24, 2015 5:09 pm
> Subject: [seqfan]  Re: Purely algorithmic number sequence identification
> 
> 
> Sounds good, how would that work? Sequencer already has a public API
> (documented at https://github.com/p-e-w/sequencer#api) so integration
> should be easy as long as Superseeker has a way to interface with a JVM
> library.
> 
> As for A122536, nothing so far I'm afraid. I really would like to run a
> mass search on sequences without formulas though. Do you perhaps know of
> a way to find just those on OEIS? Soon the batch of performance
> improvements I'm currently working on will be finished, and then
> Sequencer should be able to search all depth 6 formulas for more than
> 1000 Sequences per day. Also, a batch mode could be implemented, which
> would allow the program to process a large number of sequences at once,
> dramatically improving performance for this use case. Indeed, all of
> OEIS could be checked this way in about a week probably ? which would
> also be interesting for sequences that already *have* formulas, as some
> of them may possess interesting alternative forms, or be incorrect.
> 
> Best regards
> Philipp
> 
> 
> 
> 
> 
>> On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
>> What do you think of adding your program to Superseeker?  It sounds
> like
>> this would definitely be worth doing.
>> 
>> By the way, can you do anything with A122536?  We have 200 terms, but
> no
>> formula or recurrence!
>> 
>> Best regards
>> Neil
>> 
>> Neil J. A. Sloane, President, OEIS Foundation.
>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
> NJ.
>> Phone: 732 828 6098; home page: http://NeilSloane.com
>> Email: njasloane at gmail.com
>> 
>> 
>> On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
>> pew at worldwidemann.com> wrote:
>> 
>> > Well, it turns out the first eight elements of A000001 satisfy the,
> umm,
>> > "slightly exotic" recurrence relation
>> >
>> >   a(1) = 1
>> >   a(2) = 1
>> >   a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3
>> >
>> > ;)
>> >
>> > In earnest, while I doubt that brute forcing formulas will bring any
>> > insight into sequences that have baffled mathematicians for
> centuries
>> > with their irregularity, what might indeed be interesting is to run
> the
>> > system not on one sequence, but on tens of thousands, all of which
> have
>> > no closed-form expression associated with them (is there a way to
> query
>> > those on OEIS?). In a matter of days, Sequencer would likely return
> a
>> > hundred or so closed forms, some of which may prove correct, which
> could
>> > then be investigated rigorously.
>> >
>> > For such a search, I should probably also add a lot more
> combinatorial
>> > and number theoretic primitives to the formula generator ? whenever
> I
>> > randomly browse around OEIS, most of the sequences seem to be
> counting
>> > problems of some kind.
>> >
>> > Best regards
>> > Philipp
>> >
>> >
>> >
>> >
>> > On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
>> > > On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <
>> > olivier.gerard at gmail.com>
>> > > wrote:
>> > >
>> > > >
>> > > > It would be nice to test it on "hard" sequences and other
> sequences
>> > without
>> > > > formula.
>> > > >
>> > > >
>> > > >
>> > > For example:  http://oeis.org/A000001, the number of groups of
> order n
>> > :-)
>> > >
>> > > Or perhaps easier:  http://oeis.org/A000688, the number of abelian
>> > groups
>> > > of order n.
>> > >
>> > > _______________________________________________
>> > >
>> > > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>> >
>> >
>> > _______________________________________________
>> >
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>> 
>> _______________________________________________
>> 
>> Seqfan Mailing list - http://list.seqfan.eu/
> 
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/
> 
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/


From rselcoe at entouchonline.net  Wed Feb 25 06:35:48 2015
From: rselcoe at entouchonline.net (Bob Selcoe)
Date: Tue, 24 Feb 2015 23:35:48 -0600
Subject: [seqfan] Re: Improved lower bound for A250000
In-Reply-To: <CAEG8PYvDamRCbDj9dfC=cyeLrpYLThJGPZyCqr6QMvvt_wEKUQ@mail.gmail.com>
References: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
 <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>
 <CAEG8PYvDamRCbDj9dfC=cyeLrpYLThJGPZyCqr6QMvvt_wEKUQ@mail.gmail.com>
Message-ID: <0D1F3B422EDF45F3B72AA633DCB86882@OwnerPC>

Hi Benoit,

Excellent!  This certainly is an improvement.

But I'm having a little difficulty following how you've obtained the upper 
and lower bounds, as well as your description of coordinates.

So for my n=24 a(n)=83 board, wouldn't you also say the queens of one color 
are in the two regions x<1/4, y<1/2, x<y<x+1/3
and 1/2<x<3/4, y<x-1/3, y<1-x, while the queens of the other color are 
obtained by central symmetry (or at least something approximating central 
symmetry)???

So I don't see how the definitions between your and my configurations 
differ; that is, when you say:

>> I obtained these coefficients by equalizing the lengths of the "opposite" 
>> boundaries of the armies  (this already improves (by 1) on the "Board 4" 
>> example of the webpage).

I'm not sure what you "equalized" to gain the improvement.

But still, there is definite improvement.

I probably won't have time to look into a structural pattern for n = 4m for 
several days; my guess is one exists based on your approach, which will 
improve upon mine.  Will you have a chance to see if such a pattern exists?

Best Wishes,
Bob Selcoe

--------------------------------------------------
From: "Beno?t Jubin" <benoit.jubin at gmail.com>
Sent: Tuesday, February 24, 2015 11:25 AM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Improved lower bound for A250000

> Dear Rob,
> I improved by one the final board on the webpage by using the same idea as
> for my asymptotic bound, but you are right that in this specific case, the
> result is not centrally symmetric. From the last example on the webpage, I
> made marginal changes along the diagonals (in the [0,1]^2 coordinates)
> y=x+1/3 (deleted 3 Ws, added 5 Bs) and y=x-1/3 (deleted 4 Bs, added 4Ws):
>
> ------------------------
>
> ......WWWWWW............
>
> ......WWWWWW...........W
>
> ......WWWWWW..........WW
>
> ......WWWWWW.........WWW
>
> ......WWWWWW........WWWW
>
> ......WWWWW........WWWWW
>
> .......WWW........WWWWWW
>
> ........W.........WWWWWW
>
> ..................WWWWWW
>
> ..................WWWWW.
>
> ..................WWWW..
>
> ..................WWW...
>
> ....BB..................
>
> ...BBB..................
>
> ..BBBB..................
>
> .BBBBB..................
>
> BBBBBB..........B.......
>
> BBBBBB.........BBB......
>
> BBBBBB........BBBB......
>
> BBBBB........BBBBB......
>
> BBBB........BBBBBB......
>
> BBB.........BBBBBB......
>
> BB..........BBBBBB......
>
> B...........BBBBBB......
>
> ------------------------
>
>
>
> On Tue, Feb 24, 2015 at 6:13 PM, Rob Pratt <Rob.Pratt at sas.com> wrote:
>
>> Please share your n =24 solution.  Under the central symmetry constraint,
>> I get a maximum of 80, not 84.
>>
>> -----Original Message-----
>> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Beno?t
>> Jubin
>> Sent: Tuesday, February 24, 2015 11:50 AM
>> To: Sequence Fanatics Discussion list
>> Subject: [seqfan] Improved lower bound for A250000
>>
>> Dear seqfans,
>>
>> Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on
>> an (n,n) chessboard.
>>
>> By modifying the Pratt--Selcoe configuration, I improved the best known
>> lower bound from
>> a(n) > (9/4)*(n/4)^2
>> to
>> a(n) > (7/3)*(n/4)^2.
>> I have been sloppy with side effects, but to be on the safe side, let's 
>> say
>> a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the
>> coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the
>> following description.
>>
>> The configuration in the limit n = infinity is as follows: denoting by 
>> x,y
>> in [0,1] the coordinates on the chessboard, the queens of one color are 
>> in
>> the two regions x<1/4, y<1/2, x<y<x+1/3 and 1/2<x<3/4, y<x-1/3, y<1-x and
>> the queens of the other color are obtained by central symmetry. As you 
>> can
>> guess, I obtained these coefficients by equalizing the lengths of the
>> "opposite" boundaries of the armies (this already improves (by 1) on the
>> "Board 4" example of the webpage).
>>
>> Using an easy upper bound, one has asymptotically
>> (2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
>> Anyone to help fill the gap?
>>
>> Best,
>> Benoit
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
> 


From benoit.jubin at gmail.com  Wed Feb 25 23:10:14 2015
From: benoit.jubin at gmail.com (=?UTF-8?Q?Beno=C3=AEt_Jubin?=)
Date: Wed, 25 Feb 2015 23:10:14 +0100
Subject: [seqfan] Re: Improved lower bound for A250000
In-Reply-To: <0D1F3B422EDF45F3B72AA633DCB86882@OwnerPC>
References: <CAEG8PYuvJSkTpYMvbqCmC1bqATqq8gem9DU=hCBoe06-k_ZrEw@mail.gmail.com>
 <4e04fd9f4d874f3f82f0107dac7a2655@MERCMBX40D.na.SAS.com>
 <CAEG8PYvDamRCbDj9dfC=cyeLrpYLThJGPZyCqr6QMvvt_wEKUQ@mail.gmail.com>
 <0D1F3B422EDF45F3B72AA633DCB86882@OwnerPC>
Message-ID: <CAEG8PYvpUtYRZsQ+FL6OyixBRXXuJpWFd24fcWfF=nG6r0w9HQ@mail.gmail.com>

Dear Rob,

I think that you interpret the coordinates correctly. My configuration is
only a slight modification of yours, but not exactly the same, as you can
see in my example for n=24 (in a previous email of this conversation).
Also, the bound you give on the webpage, namely (after simplification),
a(4m) >= floor( (9/4)*m^2 + m/2 - 3/4 )
made me think that your configuration is given as follows (for n=4m):
One decomposes the chessboard into 16 smaller (m,m) chessboards as follows:
.A.B
.C.D
W.X.
Y.Z.
where the dots are empty chessboards and
A, B, C, D contain the queens of one color
and
W, X, Y, Z contain the queens of the other color.
Borrowing to the language of matrices, the occupied squares are as follows:
A: all squares,
B: strict lower-right half,
C: strict upper quarter, that is, intersection of the strict upper-left
half and the strict upper-right half,
D: upper-left half plus the first subdiagonal,
W: lower-right half,
X: intersection of the strict lower-right half minus the first subdiagonal
and the lower-left half,
Y: upper-left half,
Z: all squares minus the upper-left one.

What I meant by "equalizing the opposite boundaries" is this: in the picture

....|....|......../

....|....|......./.

....|....|....../..

....|.../....../...

....|../....../....

.....\/.......|....

..............|....

..............|.../

..............|../.

..--+.........+--..

./..|..............

/...|..............

....|..............

....|......./\.....

..../....../..|....

.../....../...|....

../......|....|....
./.......|....|....

/........|....|....

each of the lines x=1/4, x=1/2, x=3/4, y=1/2, y=x, y=x+1/3, y=x-1/3,y=1-x
borders a white region and a black region, and the length during which it
borders each is equal. This is how I optimized your solution: by
translating these lines, one adds to the army of one color while removing
from the other color (compensate this on the other pair of regions, to
still have equally sized armies), so one deduces that for the optimal
configuration of this sort, "opposite boundaries" must have same length.


I am mainly interested in asymptotics, where it does not matter whether n
is divisible by 4 or not. But for a given n, not necessarily divisible by
4, I would first draw these regions, and for any given square, if more than
half of it is within the region, I would put a queen. For the 50%-squares,
put queens for one out of the two regions. Finally (possibly not needed),
give or take a few queens on the boundaries to get an admissible
configuration.


Best,

Beno?t





On Wed, Feb 25, 2015 at 6:35 AM, Bob Selcoe <rselcoe at entouchonline.net>
wrote:

> Hi Benoit,
>
> Excellent!  This certainly is an improvement.
>
> But I'm having a little difficulty following how you've obtained the upper
> and lower bounds, as well as your description of coordinates.
>
> So for my n=24 a(n)=83 board, wouldn't you also say the queens of one
> color are in the two regions x<1/4, y<1/2, x<y<x+1/3
> and 1/2<x<3/4, y<x-1/3, y<1-x, while the queens of the other color are
> obtained by central symmetry (or at least something approximating central
> symmetry)???
>
> So I don't see how the definitions between your and my configurations
> differ; that is, when you say:
>
>  I obtained these coefficients by equalizing the lengths of the "opposite"
>>> boundaries of the armies  (this already improves (by 1) on the "Board 4"
>>> example of the webpage).
>>>
>>
> I'm not sure what you "equalized" to gain the improvement.
>
> But still, there is definite improvement.
>
> I probably won't have time to look into a structural pattern for n = 4m
> for several days; my guess is one exists based on your approach, which will
> improve upon mine.  Will you have a chance to see if such a pattern exists?
>
> Best Wishes,
> Bob Selcoe
>
> --------------------------------------------------
> From: "Beno?t Jubin" <benoit.jubin at gmail.com>
> Sent: Tuesday, February 24, 2015 11:25 AM
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Improved lower bound for A250000
>
>
>  Dear Rob,
>> I improved by one the final board on the webpage by using the same idea as
>> for my asymptotic bound, but you are right that in this specific case, the
>> result is not centrally symmetric. From the last example on the webpage, I
>> made marginal changes along the diagonals (in the [0,1]^2 coordinates)
>> y=x+1/3 (deleted 3 Ws, added 5 Bs) and y=x-1/3 (deleted 4 Bs, added 4Ws):
>>
>> ------------------------
>>
>> ......WWWWWW............
>>
>> ......WWWWWW...........W
>>
>> ......WWWWWW..........WW
>>
>> ......WWWWWW.........WWW
>>
>> ......WWWWWW........WWWW
>>
>> ......WWWWW........WWWWW
>>
>> .......WWW........WWWWWW
>>
>> ........W.........WWWWWW
>>
>> ..................WWWWWW
>>
>> ..................WWWWW.
>>
>> ..................WWWW..
>>
>> ..................WWW...
>>
>> ....BB..................
>>
>> ...BBB..................
>>
>> ..BBBB..................
>>
>> .BBBBB..................
>>
>> BBBBBB..........B.......
>>
>> BBBBBB.........BBB......
>>
>> BBBBBB........BBBB......
>>
>> BBBBB........BBBBB......
>>
>> BBBB........BBBBBB......
>>
>> BBB.........BBBBBB......
>>
>> BB..........BBBBBB......
>>
>> B...........BBBBBB......
>>
>> ------------------------
>>
>>
>>
>> On Tue, Feb 24, 2015 at 6:13 PM, Rob Pratt <Rob.Pratt at sas.com> wrote:
>>
>>  Please share your n =24 solution.  Under the central symmetry constraint,
>>> I get a maximum of 80, not 84.
>>>
>>> -----Original Message-----
>>> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Beno?t
>>> Jubin
>>> Sent: Tuesday, February 24, 2015 11:50 AM
>>> To: Sequence Fanatics Discussion list
>>> Subject: [seqfan] Improved lower bound for A250000
>>>
>>> Dear seqfans,
>>>
>>> Let a(n)=A250000(n) be the maximum size of coexisting armies of queens on
>>> an (n,n) chessboard.
>>>
>>> By modifying the Pratt--Selcoe configuration, I improved the best known
>>> lower bound from
>>> a(n) > (9/4)*(n/4)^2
>>> to
>>> a(n) > (7/3)*(n/4)^2.
>>> I have been sloppy with side effects, but to be on the safe side, let's
>>> say
>>> a(n) > (7/3)*(floor(n/4))^2 - (3+8*sqrt(2)/3)*ceiling(n/4), where the
>>> coefficient 3+8*sqrt(2)/3 is a perimeter that you can compute from the
>>> following description.
>>>
>>> The configuration in the limit n = infinity is as follows: denoting by
>>> x,y
>>> in [0,1] the coordinates on the chessboard, the queens of one color are
>>> in
>>> the two regions x<1/4, y<1/2, x<y<x+1/3 and 1/2<x<3/4, y<x-1/3, y<1-x and
>>> the queens of the other color are obtained by central symmetry. As you
>>> can
>>> guess, I obtained these coefficients by equalizing the lengths of the
>>> "opposite" boundaries of the armies (this already improves (by 1) on the
>>> "Board 4" example of the webpage).
>>>
>>> Using an easy upper bound, one has asymptotically
>>> (2+1/3)*(n/4)^2 < a(n) < 4*(n/4)^2.
>>> Anyone to help fill the gap?
>>>
>>> Best,
>>> Benoit
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>> _______________________________________________
>>>
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From gladhobo at teksavvy.com  Thu Feb 26 21:34:15 2015
From: gladhobo at teksavvy.com (Hans Havermann)
Date: Thu, 26 Feb 2015 15:34:15 -0500
Subject: [seqfan] A126263
Message-ID: <B1D27FE9-3B6B-4CA9-B2FD-D26DB357F715@teksavvy.com>

I noticed that William Stein's b-file for http://oeis.org/A126263 incorporates an incorrect a(17) that dates to the original sequence submission. One might as well add a(28) which is 73.

From peter.luschny at gmail.com  Thu Feb 26 22:27:34 2015
From: peter.luschny at gmail.com (Peter Luschny)
Date: Thu, 26 Feb 2015 22:27:34 +0100
Subject: [seqfan] Are all sufficiently large highly abundant numbers
	practical?
Message-ID: <CAMMbGZYHW0Rza6=yynvkF68JJHtUu7qRfe7WyHS4d=d1kOze3Q@mail.gmail.com>

Conjecture: (a) Every highly abundant number >10 is practical (A005153).
(b) For every integer k there exists A such that k divides a(n)
for all n>A. Daniel Fischer proved that every highly abundant
number greater than 3, 20, 630 is divisible by 2, 6, 12 respectively.
The first conjecture has been verified for the first 10000 terms.

- Jaycob Coleman, Oct 16 2013
https://oeis.org/A002093

Alaoglu and Erd?s observed that 210 is the largest highly
abundant number to include only one factor of two in its
 prime factorization. All larger highly abundant numbers
 are divisible by four, and by the argument above they
 are all practical. The remaining cases are small enough
 to test individually, and they are all practical. So
 Jaycob Coleman's conjecture is true.

- David Eppstein, 2015-02-26
http://11011110.livejournal.com/305481.html


From rkg at ucalgary.ca  Thu Feb 26 21:40:50 2015
From: rkg at ucalgary.ca (rkg)
Date: Thu, 26 Feb 2015 13:40:50 -0700 (MST)
Subject: [seqfan] A000292 (fwd)
Message-ID: <alpine.LFD.2.11.1502261339450.2122@csl.cs.ucalgary.ca>

Further apologies if you've received multiple copies of this.  R.

---------- Forwarded message ----------
Date: Thu, 26 Feb 2015 13:12:39 -0700 (MST)
From: rkg <rkg at ucalgary.ca>
To: Sequence Fans <seqfan at ext.jussieu.fr>
Subject: A000292 (fwd)

Sorry, my email has been ``upgraded'' and now my address file seems
to be all aglee.  R.

---------- Forwarded message ----------
Date: Thu, 26 Feb 2015 13:03:43 -0700 (MST)
From: rkg <rkg at ucalgary.ca>
To: Neil Sloane <njasloane at gmail.com>,
      Sloane's Dream Team <Antti.Karttunen at gmail.com>, bowerc at usa.net,
      david at research.att.com, David Wilson <davidwwilson at comcast.net>,
      deutsch at duke.poly.edu, djr at nk.ca, dwasserm at earthlink.net,
      editors at seqfan.net, j.mccranie at comcast.net, layman at math.vt.edu,
      mathar at strw.leidenuniv.nl, maxal at cs.ucsd.edu, maxale at gmail.com,
      maximilian.hasler at gmail.com, mlb at well.com, njas at research.att.com,
      noe at sspectra.com, rayjchandler at sbcglobal.net, rgwv at rgwv.com,
      rsc at swtch.com,
      simon.plouffe at gmail.com, simon.plouffe at sympatico.ca,
      somos at grail.cba.csuohio.edu, stefan.steinerberger at gmail.com,
      wasserma at spawar.navy.mil
Subject: A000292

Dear all,
          As my Mother used to say, I'm not a good looker, so
I may have missed someething in A000292.  These are not only
the triangular pyramidal numbers, but also the kind of square
pyramidal numbers you get by using cubes, and insisting that
square faces must always coincide:

1^2, 2^2, 1^2+3^2, 2^2+4^2, 1^2+3^2+5^2, 2^2+4^2+6^2, ...

           R.
1   1  1   1  1  1   1  1  1  1   1  1  1  1  1
      1  1   1  2  1   1  2  2  1   1  2  2  2  1
             1  1  1   1  2  2  1   1  2  3  2  1
                       1  1  1  1   1  2  2  2  1
                                    1  1  1  1  1



From lars.blomberg at visit.se  Fri Feb 27 07:48:50 2015
From: lars.blomberg at visit.se (Lars Blomberg)
Date: Fri, 27 Feb 2015 07:48:50 +0100
Subject: [seqfan] A254042, A254447-A254502
Message-ID: <011301d05259$7224b680$566e2380$@visit.se>



Hello!

 

The sequences A254042, A254447-A254502 are using digits 1-7 respectively.

The corresponding sequences for digits 8 and 9 seem to be missing.

Does anyone know of a reason why this is so?

If not, is it ok to add them?

 

/Lars B

 



From njasloane at gmail.com  Fri Feb 27 20:18:38 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Fri, 27 Feb 2015 14:18:38 -0500
Subject: [seqfan] Re: A254042, A254447-A254502
In-Reply-To: <011301d05259$7224b680$566e2380$@visit.se>
References: <011301d05259$7224b680$566e2380$@visit.se>
Message-ID: <CAAOnSgSuJNSQJvi=uYuXhuiHsKj+Ej4CBj8cu=Lwxy3JcujEXg@mail.gmail.com>

> If not, is it ok to add them?

Certainly!  Please do so!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Feb 27, 2015 at 1:48 AM, Lars Blomberg <lars.blomberg at visit.se>
wrote:

>
>
> Hello!
>
>
>
> The sequences A254042, A254447-A254502 are using digits 1-7 respectively.
>
> The corresponding sequences for digits 8 and 9 seem to be missing.
>
> Does anyone know of a reason why this is so?
>
> If not, is it ok to add them?
>
>
>
> /Lars B
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From peter.luschny at gmail.com  Fri Feb 27 20:47:51 2015
From: peter.luschny at gmail.com (Peter Luschny)
Date: Fri, 27 Feb 2015 20:47:51 +0100
Subject: [seqfan] Re: Are all sufficiently large highly abundant numbers
	practical?
Message-ID: <CAMMbGZbi3shQZY4v2RhE7rzGwodGVMDtjLM81CvFH+L9rPo06Q@mail.gmail.com>

The argument has been updated. Is it convincing now?

Is it appropriate for a nomination for the Riordan Prize?

Peter


From seqfan at jaycobcoleman.33mail.com  Sat Feb 28 04:37:20 2015
From: seqfan at jaycobcoleman.33mail.com (seqfan at jaycobcoleman.33mail.com)
Date: Fri, 27 Feb 2015 19:37:20 -0800 (PST)
Subject: [seqfan] Re: Are all sufficiently large highly abundant numbers
 practical?
Message-ID: <1206331671.6876.1425094640060.JavaMail.root@crow>

Hi Peter,

Coincidentally I just joined the mailing list. I will take some time to try
to understand your argument.

Sincerely,
Jaycob Coleman

On Fri, Feb 27, 2015 at 10:47 AM, Peter Luschny 'peter.luschny at gmail.com'
via 33Mail <sender at mailer.33mail.com> wrote:

> This email was sent to the alias 'seqfan at jaycobcoleman.33mail.com' by '
> seqfan at list.seqfan.eu', and 33Mail forwarded it to you. To block all
> further emails to this alias follow this link :
> http://www.33mail.com/alias/unsub/15f7de3a21d314f8a067d051ce9beea7
> Refer 2 friends to 33Mail and get a Free Premium Upgrade. Go to this url
> to get your referral link http://www.33mail.com/dashboard.
>
> The argument has been updated. Is it convincing now?
>
> Is it appropriate for a nomination for the Riordan Prize?
>
> Peter
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Supercollider? I 'ardly know 'er!


From olivier.gerard at gmail.com  Sat Feb 28 07:02:03 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Sat, 28 Feb 2015 07:02:03 +0100
Subject: [seqfan] Welcome to seqfan (was Re: Are all sufficiently large
 highly abundant numbers practical?)
Message-ID: <CAAcpPSYumjws6HCypYozGWUyewBEbXc2KcKiWBapvNg5Pgqu5g@mail.gmail.com>

On Sat, Feb 28, 2015 at 4:37 AM, <seqfan at jaycobcoleman.33mail.com> wrote:

> Hi Peter,
>
> Coincidentally I just joined the mailing list.


Dear Jaycob,

Welcome to seqfan.


> I will take some time to try
> to understand your argument.
>
> Sincerely,
> Jaycob Coleman
>
>
There are several hundreds of subscribers to seqfan.
The following advice applies to them as well:

For your future posts, please take some time to

 - ponder that your message will be archived and publicly accessible

 - consider if your message is better sent privately to a few recipients
instead of the list

 - consider if you are enhancing the signal-to-noise ratio

 - cut out non relevant parts of previous posts (everyone has received them)

 - change the subject line if you have ... changed the subject

 - check you have configured your computer and selected your email address
and provider
to avoid end signatures,  mail server messages, advertising insertions,
legal disclaimers

 - remember that the moderator cannot edit your message for you. He can only
   forward it, reject it or ask you to re-post a better version.

 - communicate directly with the administrator through
seqfan-owner at list.seqfan.eu
if you have a question about the list, your subscription, proper
netiquette, etc.

With my best regards,

Olivier G?rard
Seqfan Mailing List Administrator


> On Fri, Feb 27, 2015 at 10:47 AM, Peter Luschny 'peter.luschny at gmail.com'
> via 33Mail <sender at mailer.33mail.com> wrote:
>
> > This email was sent to the alias 'seqfan at jaycobcoleman.33mail.com' by '
> > seqfan at list.seqfan.eu', and 33Mail forwarded it to you. To block all
> > further emails to this alias follow this link :
> > http://www.33mail.com/alias/unsub/15f7de3a21d314f8a067d051ce9beea7
> > Refer 2 friends to 33Mail and get a Free Premium Upgrade. Go to this url
> > to get your referral link http://www.33mail.com/dashboard.
> >
>


From hpd at hpdale.org  Sat Feb 28 14:45:22 2015
From: hpd at hpdale.org (Harvey P. Dale)
Date: Sat, 28 Feb 2015 13:45:22 +0000
Subject: [seqfan] A102515
Message-ID: <CY1PR0401MB1068A724857277A79E884343C6120@CY1PR0401MB1068.namprd04.prod.outlook.com>

	I cannot generate the terms of the above sequence from its definition.
	Best,
	Harvey


From olivier.gerard at gmail.com  Sat Feb 28 14:53:18 2015
From: olivier.gerard at gmail.com (Olivier Gerard)
Date: Sat, 28 Feb 2015 14:53:18 +0100
Subject: [seqfan] Re: A102515
In-Reply-To: <CY1PR0401MB1068A724857277A79E884343C6120@CY1PR0401MB1068.namprd04.prod.outlook.com>
References: <CY1PR0401MB1068A724857277A79E884343C6120@CY1PR0401MB1068.namprd04.prod.outlook.com>
Message-ID: <CAAcpPSYbLk+UZK83k7mH4CXxkRYbiOtM6CoZLCC8u20kvO7TFw@mail.gmail.com>

I agree.

It seems to match

Table[1 + Floor[Sqrt[2 n - 1]], {n, 1, 83}]

instead of

Table[ Floor[Sqrt[2 n + 1]], {n, 1, 83}]


On Sat, Feb 28, 2015 at 2:45 PM, Harvey P. Dale <hpd at hpdale.org> wrote:

>         I cannot generate the terms of the above sequence from its
> definition.
>         Best,
>         Harvey
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Sat Feb 28 17:25:39 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Sat, 28 Feb 2015 11:25:39 -0500
Subject: [seqfan] Re: A102515
In-Reply-To: <CAAcpPSYbLk+UZK83k7mH4CXxkRYbiOtM6CoZLCC8u20kvO7TFw@mail.gmail.com>
References: <CY1PR0401MB1068A724857277A79E884343C6120@CY1PR0401MB1068.namprd04.prod.outlook.com>
 <CAAcpPSYbLk+UZK83k7mH4CXxkRYbiOtM6CoZLCC8u20kvO7TFw@mail.gmail.com>
Message-ID: <CAAOnSgT2tM0zEaF4K7YumKtiL-0rbqs5YxdqhPgjhkc9UaVOAw@mail.gmail.com>

please edit it accordingly!  In fact perhaps you should
replace it with two sequences (old values + new defn,
old defn + new values)!

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sat, Feb 28, 2015 at 8:53 AM, Olivier Gerard <olivier.gerard at gmail.com>
wrote:

> I agree.
>
> It seems to match
>
> Table[1 + Floor[Sqrt[2 n - 1]], {n, 1, 83}]
>
> instead of
>
> Table[ Floor[Sqrt[2 n + 1]], {n, 1, 83}]
>
>
> On Sat, Feb 28, 2015 at 2:45 PM, Harvey P. Dale <hpd at hpdale.org> wrote:
>
> >         I cannot generate the terms of the above sequence from its
> > definition.
> >         Best,
> >         Harvey
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>


From njasloane at gmail.com  Sat Feb 28 18:40:22 2015
From: njasloane at gmail.com (Neil Sloane)
Date: Sat, 28 Feb 2015 12:40:22 -0500
Subject: [seqfan] Bob Selcoe's version of the EKG and Yellowstone
 permutations A064413 and A098550
Message-ID: <CAAOnSgQcRCxm7tj24abB9B3=gsVWae4P6iuNbe9_podV1-L69Q@mail.gmail.com>

Dear Sequence Fans, Bob Selcoe recently submitted a lovely new sequence,
A255582.
Like A064413 (the EKG sequence) and A098550 (the Yellowstone Permutation,
subject of our recent arXiv:1501.01669) it is a permutation of the natural
numbers.
The definition is closer to that of A098550, but the graph is more like
that of A064413.  It would be nice to have a better understanding of
what is going on here!

Some associated sequences are A255479, A255480, A255481, A255482,
all of which need b-files, and A064664 (the inverse perm to the EKG
sequence A064413)  could
use at least a 10,000-term b-file.

Vladimir Shevelev's A254077 is of the same ilk, but here there is
no proof yet that it is a permutation of the positive integers: such a
proof is badly needed.
The cross-references in A098550 list many other related sequences that need
work.

This is all strawberry ice-cream for anyone who likes sequences.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


From 2stepan at rambler.ru  Mon Feb 23 08:59:16 2015
From: 2stepan at rambler.ru (=?koi8-r?B?wNLJyiDHxdLB08nNz9c=?=)
Date: Mon, 23 Feb 2015 07:59:16 -0000
Subject: [seqfan] 7...
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Dear SeqFans. 

Primes p such that 15p -/+ 2, 15p -/+ 4 and 15p -/+ 8 are all primes: 7, ... What in the next ( >10^9 ) one? 

P.S. 

Numbers n such that 15n -/+ 2, 15n -/+ 4 and 15n -/+ 8 are all primes: 7, 1071, 1295, 2919, 72751, ... (not in OEIS). 

Primes p such that (15p - 4, 15p - 2, 15p + 2, 15p + 4) is a prime quadruplet: 7, 13, 139, 1049, 4481, ... (not in OEIS). 

Thanks, JSG

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