[seqfan] Re: A possible characterization of A125121
David Wilson
davidwwilson at comcast.net
Sat Nov 16 06:35:53 CET 2013
Explain how 35 tiles.
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Allan
> Wechsler
> Sent: Friday, November 15, 2013 1:27 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] A possible characterization of A125121
>
> Are these also exactly those integers whose binary representations "tile"
> the integers?
>
> Represent an integer N as a set of indices S={i} such that sum 2^i = N.
> For any N we can ask: does there exist a family of shifted copies of S
which
> are (a) disjoint, and (b) whose union covers the integers? Each N poses a
> pleasant little tiling problem.
>
> I amused myself by listing the integers that tile, and found that it
matched
> A125121, whose given characterization also involves binary
representations,
> but seems quite different from my tiling description.
>
> Can anyone prove that A125121 contains exactly the integers that tile, or
find
> a counterexample?
>
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