[seqfan] Re: Voting for A250000
Lang, Wolfdieter
wolfdieter.lang at partner.kit.edu
Mon Dec 1 12:42:07 CET 2014
Dear Seq Fans:
2 votes for the (no touching) circle problem (D) A241601
1 vote for A240926 by Kival Ngaokrajang (a certain touching circle problem, together with A115032).
This proposal has put me to work.
Best regards,
Wolfdieter Lang
________________________________________
Von: SeqFan [seqfan-bounces at list.seqfan.eu] im Auftrag von Neil Sloane [njasloane at gmail.com]
Gesendet: Montag, 1. Dezember 2014 02:42
An: Sequence Fanatics Discussion list
Betreff: [seqfan] Voting for A250000
Dear Seq Fans:
Here is a list of the nominations so far.
But you can vote for any sequence received in 2014.
You have 3 votes, and you can use them up any way you want (give all to one
sequence, or split them up).
Send your votes to me.
On Dec 15 I will tally up the votes and announce the winner.
To make your life easier, here are what I consider the top 4 candidates:
The short list:
(A) A237749 The number of possible orderings of the real numbers xi*xj (i
<= j), subject to the constraint that x1 > x2 > ... > xn > 0. This (1) is
a nice sequence, (2) is easy to understand, and (3) has nice connections to
areas outside our usual focus (see the Hildebrand paper).
(B) A245783 The maximum number m such that m white queens and m black
queens can coexist on an n by n chessboard without attacking each other.
(Nice illustrations, hard but interesting problem, understandable by
anyone, has good political aspects - coexistence of rival armies. Would
appeal to journalists)
(C) A249129 Lexicographic first permutation of the nonnegative integers
such that a(2n) = a(n) + a(n+1) for all n >= 0. Very interesting sequence
in the grand tradition of recurrences that look forwards instead of
backwards. I like it a lot. I even put up a note about it in the Rutgers
Math Dept. The fact that no one has solved it in 3 weeks suggests it has
hidden depths.
(D) A241601 Number of arrangements of n circles in the affine plane.
(Lovely pictures, lovely problem, understandable by anyone, only 4 terms
known. Journalists like it.)
---------------------------------------------------
The full list:
----------------------------
>From Charles Greathouse: Nov 12 2014:
Looking through the 2014 sequences the one that jumps out at me is
A237749 The number of possible orderings of the real numbers xi*xj (i <=
j), subject to the constraint that x1 > x2 > ... > xn > 0.
which (1) is a nice sequence, (2) is easy to understand, and (3) has nice
connections to areas outside our usual focus (see the Hildebrand paper).
But this may be a bit old -- do we want to move something up 12,000 places?
(Maybe yes.)
Other sequences I liked, in no particular order:
A245970 Tower of 2s modulo n.
A241625 Smallest number m such that the GCD of the x's that satisfy
sigma(x)=m is n.
A237695 Maximum length of a +/- 1 sequence of discrepancy n.
A245783 The maximum number m such that m white queens and m black
queens can coexist on an n by n chessboard without attacking each other.
A239438 Maximal number of points that can be placed on a triangular
grid of side n so that there is no pair of adjacent points.
---------------------------
Me: Nov 13 2014:
Maybe we should allow any sequence submitted in 2014 as a candidate.
I have one nomination to make:
A249129, Lexicographic first permutation of the nonnegative integers such
that a(2n) = a(n) + a(n+1) for all n >= 0. Angelini and Haskell, Oct 21
2014. (Latt 112 p 99B)
Very interesting sequence in the grand tradition of recurrences that look
forwards instead of backwards. I like it a lot. I even put up a note about
it in the Rutgers Math Dept. The fact that no one has solved it in two
weeks suggests it has hidden depths.
[I would have liked to have nominated this next one,
but I'm not going to, since I created the entry
(although none of it is my work). It is worth adding
to anyone's "lovely problems" list.
A247000, Maximal number of palindromes in a circular binary word of length
n. Very interesting combinatorial problem.
Based on Jamie Simpson, Palindromes in circular words, Theoretical Computer
Science, Volume 550, 18 September 2014, Pages 66-78; DOI:
10.1016/j.tcs.2014.07.012.]
------------------------------------
>From Juri-Stepan Gerasimov, Nov 14 2014:
Numbers n such that n, 2^n - 1 and binomial coefficient(2^n - 1, n) are all
squarefree: 1, 2, 3, 11, 29, 31, 51, 55, 57, ... (finite)
or NO, WRONG! Primes p such that 2^p - 1 is not squarefree: 359, 397, 419,
... (infinite). JSG.
# me:
with(numtheory); a := [ ];
for n from 1 to 200 do if not issqrfree(2^n-1) then a := [ op(a), n ]; fi;
od:
which gives A049094
6, 12, 18, 20, 21, 24, 30, 36, 40, 42, 48, 54, 60, 63, 66, 72, 78, 80, 84,
90, 96, 100, 102, 105, 108, 110, 114, 120, 126, 132, 136, 138, 140, 144,
147, 150, 155, 156, 160, 162, 168, 174, 180, 186, 189, 192, 198, 200]
There is also A237043 for primitive terms. Seems to contradict Gerasimov's
suggestion.
Max A.: 2^359-1, 2^397-1, 2^419-1 are all squarefree, which can be easily
verified with http://factordb.com. So Juri's second suggestion is nonsense.
-------------------------------------
Nov 19 2014 from Gerasimov:
Numbers n such that 2n - 1 divides 2^n + 1:
1, 194997, 1463649, 1957025, ....
Best regards.
JSG
===================================================
Me: Others that I liked a lot
Multidimensional permutations: A249026
A248624 Hiccup p 94B in Latt 112
A248034 Angelini p 94A
A248410 Moewald
Lines, circles in affine plane: A241600, A241601 in Latt 111
The Angelini seq I mentioned in my talk at the OEIS Conference in October
A247665 Murthy, rel prime to next n terms
A247666 CA on hexagonal grid Latt 112 p 3
A247068 Shallit Primes with no 2 consecutive 1s
================================================
Me: A249517 (Krizek, extended by Sean Invine and then by Max) is also
pretty good.
--------------------------------
Nov 16 2014 from Michel Marcus:
I liked the Omar E. Pol series on symmetric representations of sigma :
A240062 or A239663.
But there are so many to browse ....
MM
----------------------------
>From Shevelev, Nov 16 2014:Dear Neil,
Is it worth to nominate our with Peter A246553?
(Me: This entry required a huge amount of editing)
Best regards,
Vladimir
-----------------------------------------
>From Maximilan Hasler:
On Sat, Nov 15, 2014 at 7:51 AM, Neil Sloane <njasloane at gmail.com> wrote:
> Dear Juri,
> Please submit these two sequences to the OEIS,
> and tell me the A-numbers:
>
> "Numbers n such that n, 2^n - 1 and binomial coefficient(2^n - 1, n) are
> all squarefree: 1, 2, 3, 11, 29, 31, 51, 55, 57, ... (finite)
FWIW, about a week ago I added
https://oeis.org/A245569 : Numbers n such that binomial(2^n-1,n) is
squarefree.
0, 1, 2, 3, 4, 6, 11, 12, 21, 28, 29, 31, 51, 54, 55, 57
COMMENTS
Motivated by the existence of the subsequence A246699 of squarefree
terms in this sequence.
Actually
- the additional restriction on n only removes 4 terms 4, 12, 28, 54
(for such a short sequence it could be frowned upon adding the
subsequence of squarefree terms and the further subsequence of (5)
primes.... how about subsequences of non-squarefree (in analogy to
A237043), odd and even terms ? [This was not a suggestion...])
- the other seq. (A246699, now has an additional 21 and does not have
any more "binomial" in the NAME, which makes it impossible to find it
based upon the previous mail...) says "fini"(te) without comment or
reference. I think this should be fixed.
- I don't know a reference and/or proof of the finiteness, so I
preferred to add "conjectured to be...", at the risk of exhibiting my
ignorance if this is a (well(?)) known result...
Thanks for adding such information if it exists.
Maximilian
-------------------------------------------
Dear Neil,
Let me propose an additional sequence A247190 for 250000.
Best regards,
Vladimir (Shevelev)
--------------------------------------------------------
Nov 26
I vote
http://oeis.org/A245783
Vaclav Kotesovec
--------------------------------------------------------
from jon schoenfeld, nov 30 2104
I nominate A241601 - the number of configurations of n circles in the
plane. (It's the one I computed and mentioned on the list, and you
submitted for me.) It's still a surprise to me that such a basic kind of
construction hasn't been studied before!
------------------------------------------------------
>From Zumkeller Nov 30 2014:
Dear Neil,
here are two proposals for the 250000 contest
1) https://oeis.org/A246830
2) https://oeis.org/A238880
and 1 from me (with all due modesty)
https://oeis.org/A249095,it's nice, tangible and has at least two other
nice descendants: A249133 and A249183.
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