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

[M. F. Hasler]

I think there are several sequences possible :
e.g.,

1°) the nontrivial orbits (for each k) merit to be in OEIS, maybe as
part of the sequence obtained for the least starting value leading to
the orbit ;
e.g. for k=3 the nontrivial orbit (16,48,192,18) is "first" reached
for the initial value a(0)=2,
I tentatively submit this as https://oeis.org/draft/A238984

2°) Then one could also list, for each k, the numbers that end in each
of the different cycles, trivial or not.

(Unless I'm wrong, only 1,11,111,.... end in the cycle (1).)

For k=4, there are the cycles (0), (1), (175), (384) ; any others ?
Here, starting values a(0) in {
53,135,153,375,553,579,597,753,1135,1153,1575,1755,1795,1975,3375,3515,3551,3591,3735,3951,5175,5315,5351,5391,5553,5579,5597,5711,...
}
end in (175),
(note that 175 itself does not end in 175 because of the "special rule
for less than k digits", which I interpret as "take the first digit of
the sequence if there are less then k so far")
while a(0) among
12,13,14,17,19,21,24,28,38,42,61,62,68,69,112,113,114,117,119,121,122,123,126,128,129,131,133,134,136,137,142,143,144,148,162,163,..
end in the cycle (384).

Maximilian

On Fri, Aug 1, 2014 at 6:41 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
> Hello SeqFans,
>
> 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.