A335870 a(n) is the least k > 0 such that T^k(n) = T^(2*k)(n) (where T^k denotes the k-th iterate of A006370, the Collatz map); a(n) = -1 if no such k exists.

1, 3, 3, 6, 3, 3, 6, 15, 3, 18, 6, 12, 9, 9, 15, 15, 3, 12, 18, 18, 6, 6, 15, 15, 9, 21, 9, 111, 18, 18, 18, 105, 3, 24, 12, 12, 21, 21, 21, 33, 6, 108, 6, 27, 15, 15, 15, 102, 9, 24, 24, 24, 9, 9, 111, 111, 18, 30, 18, 30, 18, 18, 105, 105, 6, 27, 27, 27, 12

Offset: 0

Author

Rémy Sigrist, Jun 28 2020

Keywords

• nonn

Comments

If the Collatz conjecture is true, then a(n) > 0 for all n >= 0.

Examples

			For n = 3 we have:
    k  T^k(3)  T^(2*k)(3)
    -  ------  ----------
    1      10           5
    2       5           8
    3      16           2
    4       8           4
    5       4           1
    6       2           2
so a(3) = 6.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Wikipedia, Floyd's Tortoise and Hare
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A139399.

Programs

PARI

a(n, T=x->if (x%2, 3*x+1, x/2)) = my (x1=n, x2=n); for (k=1, oo, x1=T(x1); x2=T(T(x2)); if (x1==x2, return (k)))