A226617 Smallest positive integer k (or 0 if no such k) with a primitive cycle of positive integers, n of which are odd including 1, under iteration by the Collatz-like 3x+k function.

1, 11, 43, 55, 643, 97, 673, 41, 1843, 329, 59, 113, 5603, 289, 6505, 77, 407, 127, 499, 79, 865, 749

Offset

1,2

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

Table of n, a(n) for n=1..22.

Example

The cycle associated with a(1)=1 is {1,2}, with a(2)=11 is {1,7,16,8,4,2}, and with a(3)=43 is {1,23,56,28,14,7,32,16,8,4,2}.

Crossrefs

Cf. A226607, A226610, A226616.

Sequence in context: A089712 A359664 A155711 * A222184 A141195 A139853

Adjacent sequences: A226614 A226615 A226616 * A226618 A226619 A226620

Keyword

nonn

Author

Geoffrey H. Morley, Jul 03 2013

Status

approved