[seqfan] Re: conjectured list of divisibility sequences
rkg at cpsc.ucalgary.ca
Mon Jan 10 21:08:45 CET 2011
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
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:
> 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> 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
> Seqfan Mailing list - http://list.seqfan.eu/
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