A226677 Smallest positive integer k (or 0 if no such k) with a primitive cycle of positive integers, exactly n of which are odd, under iteration by the Collatz-like 3x-k function.

1, 1, 11, 17, 115, 31, 1, 29, 1417, 371, 19, 23, 8977, 77, 431, 2465, 2069, 3299, 193, 451, 139, 25, 5233, 131, 1739, 10993, 3037, 121, 7061, 11329, 9479, 145, 2425, 46199, 1871, 217, 3551, 26183, 14083, 26281, 7237, 605, 181, 113, 3299, 11431, 119773, 2465

Offset: 1

Author

Geoffrey H. Morley, Jul 05 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.

Conjecture: a(n)>0 for all n.

Links

• Geoffrey H. Morley, Table of n, a(n) for n = 1..60

Crossrefs

Cf. A226626, A226661, A226676.