Rich, An early version of Superseeker did try to find a match with a linear combination of two sequences. It looked at c*A(n) + d*B(n+n_0), and tried small values of c,d,n_0 and all pairs A,B from the database. The trouble was, it was slow, it found a lot of false matches, and IIRC it never found anything useful. So I dropped it. It is certainly a project worth doing off-line though. Take all triples A, B, C of sequences and see if there is a linear dependence among them. To cut down on trivial matches, restrict A to be a sequence that has no known formula. Although the hard part would be to decide if a positive result was a known identity (which it would be most of the time) or a new discovery. Neil On Tue, Sep 23, 2014 at 3:48 PM, <rcs@xmission.com> wrote:
Looks like a fun weekend ahead!
http://dimacs.rutgers.edu/Workshops/OEIS/abstracts.html
A missing talk:
How to look hard for sequence combinations? Neil must have addressed this in Superseeker, but I haven't seen any writeup. Suppose I have generated a new sequence M(n), and it's not in OEIS. Maybe it's some combination of OEIS sequences. What's a good way to proceed? I can look for M(n) = A(n) + B(n) reasonably efficiently (assuming I have a local copy), but trying A+B+C etc. rapidly outruns available computing resources. Also, automatically rejecting false positives looks hard. This seems like a natural area for research.
Rich
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-- Dear Friends, I have now retired from AT&T. New coordinates: 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@gmail.com