A226661 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, 7, 5, 25, 13, 59, 47, 11, 29, 145, 59, 31, 115, 79, 13, 47, 5, 17, 125, 79, 263, 49, 169, 91, 191, 23, 601, 323, 193, 109, 311, 73, 149, 265, 571, 95, 491, 697, 695, 137, 29, 119, 383, 575, 283, 121, 263, 233, 163, 193, 283, 479, 107, 203, 437, 85, 491, 349

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

Geoffrey H. Morley, Table of n, a(n) for n = 1..2520

Crossrefs

Cf. A226610, A226660, A226677.

Sequence in context: A213835 A145396 A263825 * A120404 A334784 A146619

Adjacent sequences: A226658 A226659 A226660 * A226662 A226663 A226664

Keyword

nonn

Author

Geoffrey H. Morley, Jul 05 2013

Status

approved