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

Neil Sloane njasloane at gmail.com
Sun May 21 01:55:04 CEST 2017

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

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.
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
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```