A226662 Smallest positive integer k (or 0 if no such k) with conjecturally exactly n primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

1, 11, 23, 29, 5, 247, 47, 229, 13, 361, 359, 517, 481, 1669, 485, 1843, 295, 269, 233, 355, 2509, 1399, 431, 943, 1991, 4715, 7469, 3323, 1753, 2777, 781, 2347, 1201, 4741, 9233, 12607, 6559, 6721, 4879, 2359, 5531, 1805, 11773, 11113, 6755, 8861, 5897, 30079

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.

Belaga and Mignotte (2000, p.19) conjectured that the number of primitive cycles attains all positive integer values.

Links

• Geoffrey H. Morley, Table of n, a(n) for n = 1..189
• E. G. Belaga and M. Mignotte, Cyclic Structure of Dynamical Systems Associated with 3x+d Extensions of Collatz Problem, Preprint math. 2000/17, Univ. Louis Pasteur, Strasbourg (2000).

Crossrefs

Cf. A226613, A226678.