[seqfan] Re: conjectured list of divisibility sequences

[Richard Guy]

Dear All,
          I'm delighted in the current interest being shown
about divisibility sequences.  Is it not a fact that all
such sequences have a(0) = 0 ?  Also that all members of
such a sequence are divisible by  a(1),  so that, whenever
such a sequence has  a(1) > 1, it is desirable also to
list its normalized form with  a(1) = 1.  This way, people
won't miss important coincidences.  I've never understood
offsets, but it also seems desirable to include (perhaps it
already appears?) sequences such as  1,1,2,3,5,8,13,21, ...
(# of ways of tiling a  2 by n  box with dominoes), which
is not a divisibility sequence until you translate it suitably.

(Singular) sequences with zeroes should also appear.
Aren't  0,0,1,1,0,0,1,1,0,0,...  and lots of similar
sequences, which often appear in the real world, already
in there?

A paper with a three-parameter family of fourth order
divisibility sequences, infinitely many of which could
legitimately appear in OEIS, by Hugh Williams and me,
is due to appear in Internat J Number Theory.  Best,  R.

On Mon, 10 Jan 2011, Richard Mathar wrote:

>
> http://list.seqfan.eu/pipermail/seqfan/2011-January/006837.html
>
> pl> Date: Mon, 10 Jan 2011 12:05:52 +0100
> pl> From: "peter.luschny"
> pl> To: seqfan at list.seqfan.eu
> pl> Subject: [seqfan] Re: conjectured list of divisibility sequences
> pl>
> pl> I see that A000045 is not in your list and it is also
> pl> not in the OEIS index of divisibility sequences. Do I
> pl> misunderstand your definition?
>
> The Fibonacci sequence A000045 (and any sequnce a= F(n)^k, k>=1) is
> a divisibility sequence which is not in the current list because I excluded
> sequences that contain zeros (as indicated in the small print of the web page);
> A000045(0)=0 caused it to be ignored. I'll improve this part because
> not listening that "classic" example puts shame on the entire list.
>
> Richard Mathar
>
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