A226616 Smallest positive integer k for which 1 is in a primitive cycle of n positive integers (n>1) under iteration by the Collatz-like 3x+k function.

1, 5, 13, 29, 11, 17, 253, 509, 145, 43, 55, 355, 137, 1129, 1007, 131069, 97, 643, 41, 553, 281, 8388605, 4069, 4793489, 3817, 1843, 59, 113, 1301, 2155, 9397, 289, 131153, 3247, 949, 127, 77

Offset: 2

Author

Geoffrey H. Morley, Jul 02 2013

Keywords

• nonn

Comments

A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.

The 3x+k function T_k is defined by T_k(x) = x/2 if x is even, (3x+k)/2 if x is odd, where k is odd.

For primitive cycles, GCD(k,6)=1.

For n>1, T_k has a primitive cycle of length n which includes 1 when k = A036563(n) = 2^n-3. So a(n) <= 2^n-3.

Crossrefs

Cf. A226607, A226609, A226617, A226618.