# [seqfan] Re: Rewriting squares

jean-paul allouche jean-paul.allouche at imj-prg.fr
Sun May 12 18:07:58 CEST 2019

```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/

```