[seqfan] Fw: Re: Multiplication by themselves of the last k digits

[Eric Angelini]

Hello SeqFans,
Thank you to Bob, Maximilian and the others for the
interesting private mails.
I would like to clarify the P.-S. herunder (see below).
Best,
É.

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>Start S with any integer;
>Extend S with the result of the multiplication by themselves
>                                  of the last 2 digits of S;
>S always "ends" like this:
>- 0,0,0,0,0,0,0,0,0,... or
>- 1,1,1,1,1,1,1,1,1,... or
>- 2,4,8,32,6,12,(2),...
>
>Now:
>Start T with any integer;
>Extend T with the result of the multiplication by themselves
>                                  of the last 3 digits of T;
>T always "ends" like this:
>- 0,0,0,0,0,0,0,0,0,... or
>- 1,1,1,1,1,1,1,1,1,... or
>- 16,48,192,18,(16),...
>
>I didn't check U (multiplication of the last 4 digits), etc.
>Is there a sequence somewhere? [this might be old hat but
>I couldn't find anything in the OEIS]
>Best,
>É.
>
>P.-S.
>To start a seq with a single digit is easy: just multiply
>the said digit by himself - and so on.
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[Clarification]:

Let's say we start the sequence V with a(1)= 23 and that
we want to extend V by multiplying by themselves the last
5 digits of V (k=5);
We should then see the start of V as 1,1,1,23 - which gives:

V = 23,...
V = (1,1,1,)23,...
V = (1,1,1,)23,6,...
V = (1,1,1,)23,6,36,...

... and we don't need (1,1,1,) anymore from now on:

V = 23,6,36,...
V = 23,6,36,648,...

So, always start such a sequence by the necessary amount of
successive (virtual) 1's - then forget them.

Best,
É.