[seqfan] Re: Rewriting squares

[Neil Sloane]

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.
Phone: 732 828 6098; home page: http://NeilSloane.com
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
>
>
>
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>