A226678 Smallest positive integer (or 0 if no such k) with conjecturally exactly n primitive cycles of positive integers under iteration by the Collatz-like 3x-k function.

11, 17, 1, 385, 131, 193, 641, 23, 217, 7775, 57095, 3689, 1163, 14185, 8533, 467, 46199, 20143, 87089, 15217, 973, 134809, 14279

Offset: 1

Author

Geoffrey H. Morley, Jun 25 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 and k is in A226630.

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

Crossrefs

Cf. A226629, A226662.