A226676 Smallest positive integer k (or 0 if no such k) with a primitive cycle of n positive integers under iteration by the Collatz-like 3x-k function.

1, 0, 1, 11, 49, 17, 115, 473, 31, 791, 1, 29, 11491, 371, 641, 2167, 19, 119, 23, 3211, 106537, 77, 431, 2465, 2069, 5575

Offset: 1

Author

Geoffrey H. Morley, Jul 05 2013

Keywords

• nonn
• more

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.

Conjecture: For n>2, a(n)>0.

Crossrefs

Cf. A226625, A226660, A226677.