[seqfan] Re: project: looking for connections between sequences
martin.rubey at math.uni-hannover.de
Wed Aug 11 21:04:44 CEST 2010
Alexander P-sky <apovolot at gmail.com> writes:
> To start earlier without waiting for resolution of Superseeker's bottleneck,
> one might consider running NOW Martin Rubey's GUESS (free distributed) package
> (part of FriCAS - computer algebra system development).
> In my communication with Martin Rubey he indicated though that GUESS
> is only effective when hundred or more terms are available ...
Well, it depends on the search space. If you restrict to holonomic or
algebraic sequences, 30 terms is usually enough. To find an algebraic
differential equation, 100 terms would be good.
> On 8/11/10, N. J. A. Sloane <njas at research.att.com> wrote:
>> Several people have suggested that it would be interesting
>> to run the whole 200,000 sequences through Superseeker,
>> to see if there are interesting connections to be discovered.
I have checked large parts of the encyclopedia with my FriCAS package,
using various parameters, and indeed found some interesting results.
One of the more interesting is actually in the preprint, page 6 of
>> 1. a(n) is the number of .... [that is, sequences which count something]
>> 2. there is no formula given for a(n)
>> 3. at least 8 terms are known
That makes a lot of sense! In fact, I think we also discarded short
sequences. I'd say the most interesting requirement is 2.
Time is not the limiting factor with the FriCAS package. One problem
for me is to get a list of interesting sequences. In practice,
"strange" sequences (especially sparse sequences) take most of the time.
>> There will be a few thousand such sequences.
>> Then run these through Superseeker, and see if
>> they appear to be related to any of the 200,000
>> sequences in the OEIS - or if Superseeker can
>> suggest a formula or recurrence for them.
How does Superseeker find relations? In an experimental version, I have
implemented discovery of algebraic dependencies between lists of
sequences. The current version is not efficient, it would take me
another working week to finish an efficient version. I think I could do
this in september.
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