[seqfan] Re: Rewriting squares

[Kerry Mitchell]

I've played a lot with these sequences and others like them (replace each
digit x with f(x)). A couple of my favorites are (because they have both
fixed leading and trailing sequences):

   - Begin with 1 and replace each digit x with 15x. This sequence starts:
   1, 15, 1575, 157510575, etc.
   - Begin with 1 and replace each digit x with 16x: 1, 16, 1696,
   169614496, etc.
   - Begin with 3 and replace each digit x with 7^x: 3, 343, 3432401343,
   etc.

Kerry

On Sun, May 12, 2019 at 2:13 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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