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.
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
KEYWORD
nonn
AUTHOR
Geoffrey H. Morley, Jun 25 2013
STATUS
approved