# [seqfan] Re: A possible characterization of A125121

David Wilson davidwwilson at comcast.net
Sat Nov 16 23:16:17 CET 2013

```If you allow only left shift, the tileable numbers are A064896.

If you allow left and right shift, the tileable numbers are the numbers of
the form 2^m * A064896(n).
This sequence is a strict subset of the sturdy numbers A125121, with 35 the
first non-tileable sturdy number.

If you allow left shift and reversal, the tileable numbers are all odd, and
the first non-tileable odd number is 27.

If you allow left shift and right shift and reversal, the tileable numbers
are 2^m * elements of the previous sequence.

None of the last three sequences is in the OEIS.

> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of David
> Wilson
> Sent: Saturday, November 16, 2013 12:36 AM
> To: 'Sequence Fanatics Discussion list'
> Subject: [seqfan] Re: A possible characterization of A125121
>
> 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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>
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```