[seqfan] R: Seqfan Digest, Vol 4, Issue 19

vincenzo.librandi at tin.it vincenzo.librandi at tin.it
Fri Jan 30 15:12:53 CET 2009



----Messaggio originale----
Da: seqfan-request at list.seqfan.eu
Data: 
25-gen-2009 2.52 AM
A: <seqfan at list.seqfan.eu>
Ogg: Seqfan Digest, Vol 
4, Issue 19

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Today's 
Topics:

   1. Re: Q: what does A094762 count? (N. J. A. Sloane)
   2. 
Re: How to generate A000047? (Giovanni Resta)
   3. Re: [OEIS] Wrong 
comments (Richard Mathar)
   4. A152776 Numbers such that every run 
length in base 2 is 3.
      (zak seidov)
   5.  Thue-Morse Odiousness 
(Tanya Khovanova)
   6. Re: A152776 Numbers such that every run length 
in base 2	is
      3. (Maximilian Hasler)
   7. Re: [math-fun] count of 
terms in cyclotomic polynomial
      (wouter meeussen)
   8.  A033035: 
Change of parity (zak seidov)
   9.  A124677 vs A075099 (Beno?t Jubin)
  10. Re: A033035: Change of parity (zak seidov)


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

Message: 1
Date: Sat, 24 Jan 2009 01:01:59 -0500
From: "N. J. A. 
Sloane" <njas at research.att.com>
Subject: [seqfan] Re: Q: what does 
A094762 count?
To: seqfan at list.seqfan.eu
Message-ID: <200901240601.
n0O61xRe010176 at prim.research.att.com>
Content-Type: text/plain; 
charset=us-ascii

I agree with Ray:  it looks like A094761 has been 
reused - and so 
A094762 is no longer well-defined.  In any case it is 
a rather dull
sequence:  
%S A094762 
1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9

I'll wait a day or so in case 
someone has a better idea,
and then I'll kill A094762.

I did check my 
records, and I can find no mention of these
sequences in emails going 
back to 2004

Neil



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

Message: 2
Date: 
Sat, 24 Jan 2009 09:11:05 +0100
From: Giovanni Resta <g.resta at iit.cnr.
it>
Subject: [seqfan] Re: How to generate A000047?
To: Sequence 
Fanatics Discussion list <seqfan at list.seqfan.eu>
Message-ID: <497ACD19.
2080804 at iit.cnr.it>
Content-Type: text/plain; charset=ISO-8859-1; 
format=flowed

Harry J. Smith wrote:
> This program had a problem for n 
> 30. I think I have fixed it:
>   
Yes, thanks. I discovered it too, 
it was the missing cast in

(long long)D[k]*D[k]<=n;

In the meantime I 
also implemented a suggestion by
Ray Chandler which cut the time in 
two:
an odd number cannot be representable if it is
equal to 3 or 5 mod 
8.

Using that I was able to compute 
the values up to 33 in 645 
minutes. 
(Ray confirmed the values up to 32 with a Mathematica 
program).
Now I'm computing the 34th value and then I'll stop the 
program.
Each new value needs, on my PC, about 2.62 times the time for 
the
previous, so the next one will appear after 645*2.62 minutes since
I run the program, which means about 28 hours.
Since it does not seems 
that this problem is that interesting, I 
think I'll stop there and 
I'll submit the new values up to 34th to OEIS.

If , for some unknown 
reason, one really wants more values, it is worth 
noting
that this 
problem is highly parallelizable.

giovanni




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

Circa il commento di Richard J Mathar 
su odd/even, facco presente che
con la scritta "of course" naturalmente 
voglio indicare che
nella serie in oggetto appartengono sicuramente 
tutti i numeri
dispari/o pari, e non per questo non possono appartenere 
alla stessa
serie a(n) anche alcuni numeri dispari/pari, ricavati nella 
forma
triangolare "let p prime number n= ...) .

Regards, 
Vincenzo 
Librandi 
Message: 3
Date: Sat, 24 Jan 2009 16:18:52 +0100
From: 
Richard Mathar <mathar at strw.leidenuniv.nl>
Subject: [seqfan] Re: [OEIS] 
Wrong comments
To: seqfan at seqfan.eu
Message-ID: <200901241518.
n0OFIq2Q012476 at amer.strw.leidenuniv.nl>
Content-Type: text/plain; 
charset=us-ascii


bj> From seqfan-bounces at list.seqfan.eu Fri Jan 23 22:
54:35 2009
bj> Date: Fri, 23 Jan 2009 13:33:20 -0800
bj> From: =?ISO-
8859-1?Q?Beno=EEt_Jubin?= <benoit.jubin at gmail.com>
bj> To: "N. J. A. 
Sloane" <njas at research.att.com>,
bj>         Sequence Fanatics 
Discussion list <seqfan at list.seqfan.eu>
bj> Subject: [seqfan]  [OEIS] 
Wrong comments
bj> ...
bj> The wrong comment "Of course n is odd" 
appears in A154611, A153381,
bj> A153350, A153329, A153309, A153088.
bj> The wrong comment "Of course n is even" appears in A153170.
bj> 
bj> I think the author means "All odd/even numbers appear in this 
sequence".
bj> ...

These can be cured as follows:

%I A154611
%S 
A154611 
1,3,5,6,7,9,11,12,13,15,16,17,18,19,20,21,23,24,25,26,27,29,30,31,33,
%
T A154611 
35,36,37,39,41,42,43,45,46,47,48,49,51,53,54,55,56,57,59,60,61,62,63,
%
U A154611 
64,65,66,67,69,70,71,72,73,75,76,77,78,79,81,83,84,85,86,87,89,90,91
%N 
A154611 Numbers n such that 7n+3 is not prime.
%C A154611 Contains all 
odd numbers A005408 and all even numbers of the form 2*A153307(k).
%F 
A154611 Let p prime number, n=[(p^2+2p-3)/7] mod.(p); or, n=[(p^2+4p-3)
/7] mod.(p); or, n=[(p^2+12p-3)/7] mod.(p).
%e A154611 Example: 42=
[11^2+2*11-3)/7]mod.(11), 42=20 mod(11); 26=[(5^2+4*5-3)/ 7] mod.(5), 
26=6 mod.(5); 18=[(3^2+12*3-3)/7] mod.(3), 18=6 mod.(3)
%Y A154611 Cf. 
A089033, A045437, A017017
%K A154611 nonn,new
%O A154611 1,2
%A A154611 
Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 15 2009
%E A154611 
Rephrased comment on parity of n - R. J. Mathar (mathar(AT)strw.
leidenuniv.nl), Jan 24 2009


%I A153381
%S A153381 
1,2,3,4,5,7,8,9,10,11,13,14,15,17,18,19,20,21,22,23,25,26,27,29,30,31,
%
T A153381 
32,33,35,37,38,39,40,41,43,44,45,46,47,48,49,50,51,53,55,56,57,59,60,
%
U A153381 
61,62,63,65,66,67,68,69,70,71,73,74,75,76,77,79,80,81,83,85,86,87,88
%N 
A153381 Numbers n such that 11n+5 is not prime
%C A153381 The odd 
numbers A005408 are a subset.
%F A153381 Let p=prime; n=(p^2-5)/11 mod.
(p); n=(p^2+4p-5)/11 mod.(p); n=(p^2+6p-5)/ 11 mod.(p); n=(p^2+16p-5)
/11 mod.(p); n=(p^2+18p-5)/11 mod.(p);
%Y A153381 Cf. A108233
%K 
A153381 nonn
%O A153381 1,2
%A A153381 Vincenzo Librandi (vincenzo.
librandi(AT)tin.it), Dec 25 2008
%E A153381 Rephrased comment on parity 
of n - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 24 2009


%I 
A153350
%S A153350 
1,2,3,4,5,7,9,10,11,12,13,15,16,17,19,21,22,23,25,27,28,29,30,31,32,33,
%T A153350 
34,35,37,39,40,41,42,43,44,45,46,47,49,50,51,52,53,55,56,57,58,59,61,
%
U A153350 
62,63,64,65,66,67,69,70,71,72,73,74,75,76,77,79,81,82,83,85,87,88,89
%N 
A153350 Numbers n such that 7n+11 is not prime
%C A153350 The odd 
numbers A005408 are a subset.
%F A153350 Let p = prime number; n=(p^2-
11)/7 mod.(p); n=(p^2+4-11)/7 mod.(p); n=(p^2+10p-11)/ 7 mod.(p)
%F 
A153350 n=(p^2+4-11)/7 mod.(p); correct: n=(p^2+4p-11)/7 mod.(p); [From 
Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 07 2009]
%Y 
A153350 Cf. A101123
%K A153350 nonn,new
%O A153350 1,2
%A A153350 
Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 24 2008
%E A153350 
Rephrased comment on parity of n - R. J. Mathar (mathar(AT)strw.
leidenuniv.nl), Jan 24 2009


%I A153329
%S A153329 
1,3,4,5,7,9,10,11,13,15,16,17,18,19,21,22,23,24,25,27,28,29,31,32,33,
%
T A153329 
34,35,37,39,40,41,43,44,45,46,47,49,51,52,53,55,57,58,59,60,61,63,64,
%
U A153329 
65,67,68,69,70,71,72,73,74,75,76,77,78,79,81,82,83,85,87,88,89,90,91
%N 
A153329 Numbers n such that 5n+1 is not prime.
%C A153329 Contains all 
odd numbers A005408 and even numbers of the form 2*A153275(k).
%F 
A153329 Let p = prime number, n=(p^2-1)/5 mod.(p); n=(p^2+4p-1)/5 mod.
(p); n=(p^2+6p-1)/ 5 mod.(p)
%Y A153329 Cf. A024894
%K A153329 nonn
%O 
A153329 1,2
%A A153329 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
Dec 23 2008
%E A153329 Rephrased comment on parity of n - R. J. Mathar 
(mathar(AT)strw.leidenuniv.nl), Jan 24 2009

%I A153309
%S A153309 
1,3,5,7,8,9,11,13,15,16,17,18,19,21,23,25,27,28,29,30,31,33,35,37,38,
%
T A153309 
39,40,41,43,44,45,47,48,49,51,53,55,56,57,58,59,61,62,63,65,67,68,69,
%
U A153309 
71,72,73,75,77,78,79,81,82,83,84,85,86,87,88,89,91,93,95,96,97,98,99
%N 
A153309 Numbers n such that 3n+1 is not prime
%C A153309 Contains all 
odd numbers A005408 and even numbers of the form 2*A046954(k).
%F 
A153309 Let p = prime number, n=(p^2-1)/3 mod.(p)
%Y A153309 Cf. 
A024892
%Y A153309 Adjacent sequences: A153306 A153307 A153308 
this_sequence A153310 A153311 A153312
%K A153309 nonn
%O A153309 1,2
%A 
A153309 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 23 2008
%E 
A153309 Rephrased comment on parity of n - R. J. Mathar (mathar(AT)strw.
leidenuniv.nl), Jan 24 2009

%I A153088
%S A153088 
1,2,3,5,7,8,9,10,11,13,14,15,17,19,20,21,23,24,25,26,27,29,31,32,33,34,
%T A153088 
35,37,38,39,41,42,43,44,45,47,49,50,51,52,53,55,56,57,58,59,60,61,62,
%
U A153088 
63,64,65,66,67,68,69,71,73,74,75,77,79,80,81,83,85,86,87,89,91,92,93
%N 
A153088 Numbers n such that 5n-1 is not prime
%C A153088 Contains all 
odd numbers A005408 and even numbers of the form 2*(A153380(k)+1).
%F 
A153088 Let p=prime number, n=(p^2+1)/5 mod.(p); or, n=(p^2+2p+1)/5 mod.
(p); or, n=(p^2+8p+1/5 mod.(p)
%Y A153088 Cf. A153355
%K A153088 nonn,
new
%O A153088 1,2
%A A153088 Vincenzo Librandi (vincenzo.librandi(AT)
tin.it), Jan 03 2009
%E A153088 First 29 replaced by 20, 4 replaced by 
44, extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 05 
2009. Comment corrected, Jan 24 2009


%I A153170
%S A153170 
2,4,6,8,10,11,12,14,16,18,20,21,22,24,25,26,28,30,31,32,34,36,38,39,40,
%T A153170 
41,42,44,46,47,48,50,51,52,53,54,56,58,60,61,62,64,66,67,68,69,70,71,
%
U A153170 
72,73,74,76,78,80,81,82,84,86,88,90,91,92,94,95,96,98,99,100,101,102
%N 
A153170 Numbers n such that 3n+2 is not prime
%C A153170 Contains all 
strictly positive even numbers of A005843 and the odd numbers of the 
form 2*A059324(k)+1.
%F A153170 Let p prime number n=[(p^2+2p-2)/3] mod.
(2p); (For columns of sound odd place) n=[(p^2+4p-2)/3] mod.(2p); (For 
columns of sound even place)
%e A153170 *; *, *; *, 11, *; *, *, *, *; 
*, *, 25, *, *; *, 21, *, *, 47, *; *, *, *, *, *, *, *; *, *, 39, *, 
*, 73, *, *; *. 31, *, *, 69, *, *, 107, *;
%Y A153170 Cf. A024893
%K 
A153170 nonn
%O A153170 1,1
%A A153170 Vincenzo Librandi (vincenzo.
librandi(AT)tin.it), Dec 20 2008
%E A153170 Rephrased comment on parity 
of n, changed 2nd 30 to 40. - R. J. Mathar (mathar(AT)strw.leidenuniv.
nl), Jan 24 2009




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

Message: 4
Date: 
Sat, 24 Jan 2009 07:27:29 -0800 (PST)
From: zak seidov <zakseidov at yahoo.
com>
Subject: [seqfan] A152776 Numbers such that every run length in 
base 2
	is 3.
To: seqfan at seqfan.eu
Message-ID: <95733.10023.qm at web38201.
mail.mud.yahoo.com>
Content-Type: text/plain; charset=us-ascii


A152776 Numbers such that every run length in base 2 is 3.

a(1) = 7; a
(n) = 8*a(n - 1) + 7*mod(n, 2)

First 100 terms:

http://zak08.
livejournal.com/4851.html


      



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

Message: 5
Date: Sat, 24 Jan 2009 09:41:21 -0800 (PST)
From: Tanya 
Khovanova <mathoflove-seqfan at yahoo.com>
Subject: [seqfan]  Thue-Morse 
Odiousness
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.
eu>
Message-ID: <836648.10862.qm at web65402.mail.ac4.yahoo.com>
Content-
Type: text/plain; charset=iso-8859-1

Dear SeqFans,

I finished another 
blog entry about sequences: Thue-Morse Odiousness:
http://blog.
tanyakhovanova.com/?p=97

I think there is a lot of potential for 
putridity sequences.

I apologize for being stupid and not creating a 
sequences category
earlier. I write a lot about sequences and only now 
realized "What was
I thinking?" and created this category.

I marked my 
previous entries related to sequences and now the sequences
category 
contains 13 entries.

Tanya




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

Message: 6
Date: Sat, 24 Jan 2009 14:14:19 -0400
From: Maximilian 
Hasler <maximilian.hasler at gmail.com>
Subject: [seqfan] Re: A152776 
Numbers such that every run length in
	base 2	is 3.
To: Sequence 
Fanatics Discussion list <seqfan at list.seqfan.eu>
Message-ID:
	
<3c3af2330901241014k774f5705t463496de4b248fe9 at mail.gmail.com>
Content-
Type: text/plain; charset=ISO-8859-1

that's 7*A033118

On Sat, Jan 24, 
2009 at 11:27 AM, zak seidov <zakseidov at yahoo.com> wrote:
>
> A152776 
Numbers such that every run length in base 2 is 3.
>
> a(1) = 7; a(n) = 
8*a(n - 1) + 7*mod(n, 2)
>
> First 100 terms:
>
> http://zak08.
livejournal.com/4851.html
>
>
>
>
>
> 
_______________________________________________
>
> Seqfan Mailing list 
- http://list.seqfan.eu/
>



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

Message: 
7
Date: Sat, 24 Jan 2009 23:08:44 +0100
From: "wouter meeussen" <wouter.
meeussen at pandora.be>
Subject: [seqfan] Re: [math-fun] count of terms in 
cyclotomic
	polynomial
To: "math-fun" <math-fun at mailman.xmission.com>,	
"SeqFan"
	<seqfan at list.seqfan.eu>
Message-ID: 
<004001c97e70$52e44ba0$c887c554 at pcwou>
Content-Type: text/plain;	
charset="iso-8859-1"

if seq_z(n)  equals   mu(n) Sum(d|n,  phi(d) mu
(d) )
then, for all sqarefree n, with prime decomposition p*q*r*..*z
seq_z[n] = (p-2)*(q-2)*(r-2)*...*(z-2)

still boring?

W.




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

Message: 8
Date: Sat, 24 Jan 2009 16:21:
01 -0800 (PST)
From: zak seidov <zakseidov at yahoo.com>
Subject: 
[seqfan]  A033035: Change of parity
To: seqfan at seqfan.eu
Message-ID: 
<938840.21849.qm at web38206.mail.mud.yahoo.com>
Content-Type: text/plain; 
charset=us-ascii

Change of parity in A033035:
{7, 10}
{70, 91}
{637, 
820}
{5740, 7381}
{51667, 66430}
{465010, 597871}
Anyone may wish to 
check/add terms?
and submit to Neil?
thx, zak


      



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

Message: 9
Date: Sat, 24 Jan 2009 17:19:
15 -0800
From: Beno?t Jubin <benoit.jubin at gmail.com>
Subject: [seqfan]  
A124677 vs A075099
To: seqfaneu <seqfan at seqfan.eu>
Message-ID:
	
<79b0f44e0901241719ofe00939n6e646c0ff9600dec at mail.gmail.com>
Content-
Type: text/plain; charset=ISO-8859-1

The sequences A075099 and A124677 
have the same definition but not the
same values.

I would leave 
A075099 unchanged, that is:
%N A075099 Minimal total number of 
multiplications needed to generate
all words of length n in the free 
monoid on two generators.
and write for the other:
%N A124677 Minimal 
total number of multiplications by one-letter words
needed to generate 
all words of length n in the free monoid on two
generators, considering 
that a one-letter word needs one
multiplication
(as far as I understand 
it)

Also, in %e A124677, the expression a(3)=11 should be replaced by a
(3)=13.

Also, for
%E A075100 Shouldn't a(2) = 2 ? Shouldn't a(3) = 5, 
because we need x,
y, xx, xy, yy ? I'm confused! - njas, Dec 25 2006
I 
think the confusion comes from the fact that njas counts the
one-letter 
words, so obtains always the written value plus 2.
I think njas's way 
of counting is preferable, so the terms should be
changed accordingly.

Actually, maybe we should replace "free monoid" by "free semigroup" in
the definitions of A075099 and A075100 (which both have offset 1, and
not 0) to make it clearer.

Benoit



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

Message: 10
Date: Sat, 24 Jan 2009 17:52:10 -0800 (PST)
From: zak 
seidov <zakseidov at yahoo.com>
Subject: [seqfan] Re: A033035: Change of 
parity
To: seqfan at seqfan.eu
Message-ID: <268904.90125.qm at web38201.mail.
mud.yahoo.com>
Content-Type: text/plain; charset=us-ascii

1. More 
terms:
{4185097,5380840}
{37665880, 48427561}

2a. First terms in pairs 
==0 (mod 7), and
2b.  last terms in pairs ==1 (mod 9).

--- On Sat, 
1/24/09, zak seidov <zakseidov at yahoo.com> wrote:

> From: zak seidov 
<zakseidov at yahoo.com>
> Subject: [seqfan]  A033035: Change of parity
> 
To: seqfan at seqfan.eu
> Date: Saturday, January 24, 2009, 7:21 PM
> 
Change of parity in A033035:
> {7, 10}
> {70, 91}
> {637, 820}
> {5740, 
7381}
> {51667, 66430}
> {465010, 597871}
> Anyone may wish to 
check/add terms?
> and submit to Neil?
> thx, zak
> 
> 
>       
> 
> 
> _______________________________________________
> 
> Seqfan Mailing 
list - http://list.seqfan.eu/


      



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

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