[seqfan] Re: Knights-move Ulam-Warburton - nice problem
Allan Wechsler
acwacw at gmail.com
Mon Dec 17 02:58:57 CET 2018
The graphs of the difference sequences (A319019, A322050) strongly suggest
some kind of self-similarity under the a map that takes 1+n to 1+2n. This
is a very vague hint as to a possible direction of work.
Would it be possible to change the scatterplot from logarithmic to linear?
I have a feeling the logarithmic representation is hiding a lot of
possibly-suggestive structure near the upper rim of the graph. Also, I see
a lot of vaguely log-n-shaped curves, which would be straight lines in a
linear representation.
On Sun, Dec 16, 2018 at 6:31 PM Hugo Pfoertner <yae9911 at gmail.com> wrote:
> Neil, all,
>
> using Remy's b-file I get the following for the number of agreeing terms in
> the rows:
> Start
> agreeing
> first non-matching pair
> 3 1 5 1
> 5 1 7 5
> 9 2 6 3
> 17 4 8 5
> 33 6 17 15
> 65 11 145 141
> 129 22 73 69
> 257 43 734 726
> 513 86 349 341
> 1025 171 3579 3563
> 2049 342 1696 1680
> 4097 683 17810 17778
> 8193 1366 8394 8362
> 16385 2731 88553 88489
> 32769 5462 41665 41601
>
> After the row starting at position 33,
> the pattern of the match counts a(k) seems to be
> 2*a(k-1) if a(k-1) is odd, else 2*a(k-1)-1
>
> Regards
> Hugo
>
> On Sun, Dec 16, 2018 at 6:08 PM Neil Sloane <njasloane at gmail.com> wrote:
>
> > Dear Seq Fans, Someone who watched the Terrific Toothpicks Numberphile
> > video on Youtube suggested a knights-move version. I looked this up in
> the
> > OEIS of course and found that Remy Sigrist had already studied it. The
> > illustrations (excluding mine) are lovely, and so is the problem.
> > The original sequences are A319018, A319019; while trying to analyze it I
> > added three more last night, A322048, -049, -050.
> >
> > The main problem to crack is what is A322049.(which gives the growth from
> > the corners of the octagon after a power of 2 generations)?
> >
> > It would be nice to have a really big b-file (or a-file or both) for
> > A322050.
> >
> > Another question: look at the rows of the triangle in A322050. They are
> > converging to the sequence A322049. The number of terms in rows
> 1,2,3,4,...
> > that agree with the limit are 1,1,2,4,7,11,22 (I think). How does this
> > continue? This is not yet in the OEIS.
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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