A268731 - OEIS

%I #11 Nov 19 2023 21:17:19

%S 1,6,1,1,1,1,1,18,1,6,1,1,16,16,1,1,1,1,6,6,1,1,1,22,1,3,1,1,1,13,1,6,

%T 6,6,6,6,6,16,1,108,1,28,1,1,1,6,2,1,1,1,2,2,6,6,18,1,18,1,18,18,53,

%U 53,1,3,3,3,6,6,6,16,2,22,2,6,2,2,6,6,1,2,2,2

%N Period of the decimal expansion of 1/h(n) where h(n) is the length of the finite sequence {n, f(n), f(f(n)),...,1} in the Collatz (or 3n + 1) problem.

%C a(n) = A007732(A006577(n)).

%H Michel Lagneau, <a href="/A268731/b268731.txt">Table of n, a(n) for n = 2..9999</a>

%e a(3) = 6 because A007732(A006577(3)) = A007732(7) = 6.

%t f[n_]:=Module[{a=n,k=0},While[a!=1,k++;If[EvenQ[a],a=a/2,a=a*3+1]];k]; Table[r = f[n]/2^IntegerExponent[f[n], 2]/5^IntegerExponent[f[n], 5]; MultiplicativeOrder[10, r], {n, 2,100}]

%Y Cf. A006577, A007732.

%K nonn,base

%O 2,2

%A _Michel Lagneau_, Feb 12 2016