[seqfan] Re: A problem for digit sum of n in base 3

jens at voss-ahrensburg.de jens at voss-ahrensburg.de
Tue Apr 3 14:22:20 CEST 2012

Sorry, Vladimir, but this seems to be a case of the
http://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers:

For n=10, s(1024) = 8, s(1032) = 6, s(1030) = 6, ... (stabilization),
but n-1 = 9 is not a Fibonacci number.

Regards,
Jens

> Dear SeqFans,
>
> Let s(n)=s_3(n) be digit sum of n in base 3. Consider iterations: a_1(n)
=s
> (2^n), a_2(n)=s(2^n+a_1(n)),
> a_3(n)=s(2^n+a_2(n)),...
> Question. For which n there exists N=N(n) such that, for k>N, a_k(n)
=consta
> nt(k)?
> It is interesting that for a few small n such a stabilization arises
only w
> hen n-1 is a FIBONACCI number.
> I am not sure that it is kept for larger n. If anyone can verify that?
> Examples. For n=5, s(32)=4, s(36)=2, s(34)=4, s(36)=2,... (without
stabiliz
> ation);
>                 For n=6, s(64)=4, s(68)=6, s(70)=6, s(70)=6,... (st
> abilization)
>
> Regards,
>
>
>
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>
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