[seqfan] Re: Purely algorithmic number sequence identification

Philipp Emanuel Weidmann pew at worldwidemann.com
Tue Feb 24 21:37:36 CET 2015


Sounds good, how would that work? Sequencer already has a public API
(documented at https://github.com/p-e-w/sequencer#api) so integration
should be easy as long as Superseeker has a way to interface with a JVM
library.

As for A122536, nothing so far I'm afraid. I really would like to run a
mass search on sequences without formulas though. Do you perhaps know of
a way to find just those on OEIS? Soon the batch of performance
improvements I'm currently working on will be finished, and then
Sequencer should be able to search all depth 6 formulas for more than
1000 Sequences per day. Also, a batch mode could be implemented, which
would allow the program to process a large number of sequences at once,
dramatically improving performance for this use case. Indeed, all of
OEIS could be checked this way in about a week probably – which would
also be interesting for sequences that already *have* formulas, as some
of them may possess interesting alternative forms, or be incorrect.

Best regards
Philipp





On Tue, 2015-02-24 at 08:17 -0500, Neil Sloane wrote:
> What do you think of adding your program to Superseeker?  It sounds like
> this would definitely be worth doing.
> 
> By the way, can you do anything with A122536?  We have 200 terms, but no
> formula or recurrence!
> 
> Best regards
> Neil
> 
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
> 
> 
> On Mon, Feb 23, 2015 at 1:21 PM, Philipp Emanuel Weidmann <
> pew at worldwidemann.com> wrote:
> 
> > 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.
> > >
> > > _______________________________________________
> > >
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> >
> >
> >
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> >
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> >
> 
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