[seqfan] Re: Purely algorithmic number sequence identification

[Philipp Emanuel Weidmann]

Well, it turns out the first eight elements of A000001 satisfy the, umm,
"slightly exotic" recurrence relation

  a(1) = 1
  a(2) = 1
  a(n) = Floor(a(n-2)*(2-Sin(2^n)))   for n >= 3

;)

In earnest, while I doubt that brute forcing formulas will bring any
insight into sequences that have baffled mathematicians for centuries
with their irregularity, what might indeed be interesting is to run the
system not on one sequence, but on tens of thousands, all of which have
no closed-form expression associated with them (is there a way to query
those on OEIS?). In a matter of days, Sequencer would likely return a
hundred or so closed forms, some of which may prove correct, which could
then be investigated rigorously.

For such a search, I should probably also add a lot more combinatorial
and number theoretic primitives to the formula generator – whenever I
randomly browse around OEIS, most of the sequences seem to be counting
problems of some kind.

Best regards
Philipp




On Mon, 2015-02-23 at 11:02 -0500, W. Edwin Clark wrote:
> On Mon, Feb 23, 2015 at 5:42 AM, Olivier Gerard <olivier.gerard at gmail.com>
> wrote:
> 
> >
> > It would be nice to test it on "hard" sequences and other sequences without
> > formula.
> >
> >
> >
> For example:  http://oeis.org/A000001, the number of groups of order n :-)
> 
> Or perhaps easier:  http://oeis.org/A000688, the number of abelian groups
> of order n.
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/