[seqfan] Re: More about lex earliest cubefree 0,1 sequence

[Neil Sloane]

Maximilian,  I thought that there was no proof that your algorithm works.

(We had an email discussion about this)

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 Sat, May 20, 2017 at 7:13 PM, M. F. Hasler <seqfan at hasler.fr> wrote:

> On Sun, May 21, 2017 at 12:02 AM, Antti Karttunen <
> antti.karttunen at gmail.com
> > wrote:
>
> > Dear M. F. Hasler,
> > in the algorithm you describe in http://oeis.org/A282317 ?
> > That is, how much shorter (than the previous total length of S) each new
> > added segment W is at each "approximate doubling" step?
>
> Is there any regularity to this sequence?
> >
>
> Antti,
> thanks for your interest in this.
> Yes, indeed there is a pseudo-regularity:
> I have just submitted https://oeis.org/draft/A286940 with the length of
> the
> words appended at the n-th step (a(0...2) being somehow arbitrary).
>
> The sequence starts
>
> 1, 1, 1, 3, 2, 7, 15, 13,
>
> 1, 42, 39, 42, 39, 42, 28,
>
> 1, 42, 39, 42, 39, 42, 28,
>
> 1, 42, 39, 42, 39, 35, 7, 32, 7, 35, 7, 32, 7, 35, 7, 32, 4,
>
> 39, 42, 39, 42, 39, 35, 7, 32, 7, 35, 7, 32, 7, 35, 7, 32, 4,
>
> 39, 42, 39, 42, 39, 35, 7, 32, 7, 35, 7, 32, 7, 35, 7, 32, 4, 28,
>
> 1, 42, 39, 42, 39, 42, 28,
>
> 1, 42, 39, 42, 39, 42, 28,
>
> 1, 42, 39, 42, 39, 35, 7, 32, 7, 35, 7, 32, 7, 35, 7, 32, 4,
>
> 39, 42, 39, 42, 39, 35, 7, 32, 7, 35, ...
>
> --
> Maximilian
>
> --
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>