[seqfan] Re: Number of k-divided sequences (corrected)

[hv at crypt.org]

Neil Sloane <njasloane at gmail.com> wrote:
:Hugo, Your version is also very interesting.
:And is a lot more pleasing to think about (however, it isn't
:the definition that pops out of Shirshov's theorem).
:
:So it would be interesting if you produced analogs of
:the sequences listed in A210109 that were based on your notion.
:
:Also, if you have programs for your version, I would
:very much like to see them. This investigation is connected
:to a problem that my colleague David Applegate and I
:have been working on.

Please see <https://github.com/hvds/seq/tree/master/k-steppable>
for a repository with perl and C code to evaluate these sequences.

Results for 2 <= b <= 4; 2 <= k <= 5; k <= n <= 16, b^n < 2^32
are recorded in the 'results' file there, but I'm not sure what sequences
I can most usefully export from that.

Sadly, looking through those links I see my documentation is not up
to scratch; I'll try to improve that over the next day or two. The
code is however relatively simple, and the commits advancing from
simplistic to minor optimizatoin should help to clarify.

Hugo