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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.
2
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
1,2
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
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
Sequence in context: A225587 A143584 A134773 * A205714 A061752 A122259
KEYWORD
nonn
AUTHOR
Geoffrey H. Morley, Jun 25 2013
STATUS
approved