# [seqfan] Re: Rewriting squares

Neil Sloane njasloane at gmail.com
Wed May 15 21:01:41 CEST 2019

```I've created A308170 and A308171 for Jeremy's two sequences.

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 Sun, May 12, 2019 at 12:08 PM jean-paul allouche <
jean-paul.allouche at imj-prg.fr> wrote:

> Hi
>
> By the definition itself, the infinite sequence is obtained by iterating
> a morphism
> (in the usual sens in combinatorics on words). For example, starting with 6
> is exactly iterating the morphism
>
> 6 --> 63
> 3 --> 9
> 9 --> 18
> 8 --> 46
> 1 --> 1
> 4 --> 61
>
> which gives 6 --> 63 --> 639 --> 63918 --> 63918146...
>
> best wishes
> jean-paul
>
> Le 12/05/2019 à 14:22, Neil Sloane a écrit :
> > It is certainly interesting.  We should have the two limiting sequences
> in
> > the OEIS:
> >
> >
> 6,3,9,1,8,1,4,6,1,6,1,6,3,1,6,3,1,6,3,9,1,6,3,9,1,6,3,9,1,8,1,6,3,9,1,8,1,6,
> > 3,9,1,8,1,4,6,1,6,3,9,1,8,1,4,6,1,6,3,9,1,8, ...
> >
> > or in the case of 25,
> >
> >
> 5,2,4,6,1,6,3,1,6,3,9,1,6,3,9,1,8,1,6,3,9,1,8,1,4,6,1,6,3,9,1,8,1,4,6,1,6,1,
> > 6,3,1,6,3,9,1,8,1,4,6,1,6,1,6,3,1,6,3,1,6,3, ...
> >
> > Also the number of steps to reach the limit cycle when starting from n,
> if
> > that looks like a reasonable sequence.
> >
> >
> >
> > 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 Sun, May 12, 2019 at 5:13 AM Jeremy Gardiner via SeqFan <
> > seqfan at list.seqfan.eu> wrote:
> >
> >> Beginning with a two-digit square, successively replace each digit with
> its
> >> square, then repeat.
> >>
> >> For example,
> >>                                    9
> >>                                   81
> >>                                  641
> >>                                36161
> >>                              9361361
> >>                           8193619361
> >>                      641819361819361
> >>              36161641819361641819361
> >> 93613613616164181936136161641819361
> >>
> >> The digits settle into a fixed sequence.
> >>
> >> Reading from the right we have (with leading 1 in the case of 7 and 9)
> >>
> >>
> >>
> 6,3,9,1,8,1,4,6,1,6,1,6,3,1,6,3,1,6,3,9,1,6,3,9,1,6,3,9,1,8,1,6,3,9,1,8,1,6,
> >> 3,9,1,8,1,4,6,1,6,3,9,1,8,1,4,6,1,6,3,9,1,8, ...
> >>
> >> or in the case of 25,
> >>
> >>
> >>
> 5,2,4,6,1,6,3,1,6,3,9,1,6,3,9,1,8,1,6,3,9,1,8,1,4,6,1,6,3,9,1,8,1,4,6,1,6,1,
> >> 6,3,1,6,3,9,1,8,1,4,6,1,6,1,6,3,1,6,3,1,6,3, ...
> >>
> >> Is this interesting, or too artificial for OEIS?
> >>
> >> Thanks,
> >> Jeremy Gardiner
> >>
> >>
> >>
> >> --
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```