[seqfan] Sequences with simple recurrence definitions

Robert Munafo mrob27 at gmail.com
Mon Nov 30 12:11:24 CET 2009

I think this topic deserves more discussion in general. If you discussed it
years ago, I think it deserves re-visiting.

There are, of course, an extremely large number of sequences that are
defined by simple recurrence relations. I have cataloged about 1000 of the
simplest of them at http://www.mrob.com/pub/math/MCS.html

Each of them has a uniquely defined number that you can look up, for example
if you put "MCS31008" into Google you will find the central polygonal
numbers 2, 4, 7, 11, 16, ... given by A[n]=n(n+1)/2+1 or various recurrence
relations. This sequence is listed in OEIS twice, as A000124 and A152947.

Superseeker does not discover recurrence-relation definitions on its own. I
wrote my own program to do that task a few years ago.

There are hundreds of sequences in my catalog which one could theoretically
submit to OEIS, but I don't see the point, because:

 *Where do you draw the line? *My catalog has completely arbitrary limits
and I could see the benefit of a catalog hundreds of times larger.*
 *How do I know that one sequence is useful and another isn't?* I have given
complexity scores to the recurrence relations, but many with low scores seem
useless and aren't in OEIS, and of course many very useful OEIS sequences
have a very complex formula.

*  Simply finding definitions and computing the terms is trivial.* My search
program generates and tests millions of sequences per second.

Alois Heinz wrote:
> I do not see any reason for any of the sequences to be listed in the OEIS.
And the author gives us no reason and no explanation, information or
> The sequence seems arbitrary and it is very simple, the given recursive
formula is too complicated.
> [...]

 Robert Munafo  --  mrob.com

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