A268731 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.

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

Offset: 2

Author

Michel Lagneau, Feb 12 2016

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Michel Lagneau, Table of n, a(n) for n = 2..9999

Crossrefs

Cf. A006577, A007732.

Programs

Mathematica

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}]