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%I #8 Mar 05 2013 13:23:08
%S 1,4,4,4,4,1,4,4,4,4,4,20,20,20,20,4,20,20,20,20,4,20,20,20,20,2,20,
%T 20,20,20,4,20,20,20,20,4,20,20,20,20,4,20,20,20,20,4,20,20,20,20,1,
%U 20,20,20,20,4,20,20,20,20,4,20,20,20,20,4,20,20,20,20
%N Consider the iteration k -> 3*k mod 10^(number of decimal digits in n). Sequence gives the number of times the iteration has to be applied to n before returning to n.
%C Pickover called a sequence of this type an "Odin sequence". It seems that a(n) = 4*5^(A055642(n) - 1) whenever n mod 5 <> 0.
%D Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 124.
%H Nathaniel Johnston, <a href="/A190338/b190338.txt">Table of n, a(n) for n = 0..10000</a>
%p a := proc(n) local c,k: c:=0:k:=n: do k:=3*k mod (10^length(n)):c:=c+1: if(k=n)then return c: fi: od: end: seq(a(n),n=0..150);
%t Flatten[Table[Position[NestList[Mod[3#,10^IntegerLength[n]]&,n,40],n][[2]]-1,{n,0,70}]] (* _Harvey P. Dale_, Mar 05 2013 *)
%Y Cf. A055642.
%K nonn,easy,base
%O 0,2
%A _Nathaniel Johnston_, May 09 2011
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