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A226670 Record-breaking values, for increasing positive integers k == 1 or 5 mod 6, of the conjectured length of the longest primitive cycle(s) of positive integers under iteration by the Collatz-like 3x+k function. 4
2, 27, 31, 43, 65, 66, 100, 106, 118, 136, 140, 141, 162, 200, 222, 262, 426, 476, 526, 636, 737, 1922, 2254, 4531, 4686, 5194, 5945, 9946, 10702, 14219, 16340, 19904, 37582, 40983, 49711, 63330 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
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
k = A226671(n). The smallest integer in the T_k cycle(s) associated with a(n) is A226672(n).
Sequence in context: A259789 A357842 A041883 * A277542 A273844 A294678
KEYWORD
nonn
AUTHOR
Geoffrey H. Morley, Jun 16 2013
EXTENSIONS
Definition clarified by Geoffrey H. Morley, Jun 23 2013
STATUS
approved

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Last modified June 25 10:55 EDT 2024. Contains 373701 sequences. (Running on oeis4.)