[seqfan] Re: Voting for A250000

Wed Dec 3 18:44:02 CET 2014

Dear Neil,

I cast my 3 votes for (D) A241601 Number of arrangements of n circles in
the affine plane.

Cheers,

Edwin

On Sun, Nov 30, 2014 at 8:42 PM, Neil Sloane <njasloane at gmail.com> wrote:

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