A226686 Conjectured record-breaking lengths, for ascending positive integers k, of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function.

11, 17, 19, 34, 69, 84, 85, 168, 171, 176, 179, 228, 252, 285

Offset: 1

Author

Geoffrey H. Morley, Jun 16 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.

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

Crossrefs

k = A226687(n). The smallest integer in the T_k cycle(s) associated with a(n) is A226688(n).

Cf. A226625, A226670.