

A226613


a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatzlike 3x+k function, where n=floor(k/3)+1.


10



1, 5, 1, 2, 9, 2, 1, 3, 2, 4, 1, 2, 3, 1, 1, 7, 1, 1, 3, 7, 2, 1, 1, 7, 3, 1, 4, 3, 1, 1, 3, 3, 2, 7, 2, 1, 1, 1, 2, 5, 2, 4, 2, 3, 2, 5, 1, 3, 3, 2, 2, 1, 1, 4, 2, 3, 2, 2, 7, 1, 3, 1, 2, 3, 4, 1, 2, 2, 1, 4, 1, 3, 2, 1, 2, 1, 8, 19, 3, 4, 2, 2, 6, 2, 3, 3, 7, 3
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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.


LINKS

Geoffrey H. Morley, Table of n, a(n) for n = 1..6667
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). [Table 1 on page 19 gives a(1) to a(500).]


FORMULA

a(n) = A226612(n+1)  A226612(n).


CROSSREFS

a(n) is the number of terms in the nth row of A226607 to A226611.
Cf. A226629, A226663.
Sequence in context: A021199 A073324 A021665 * A274989 A289690 A088781
Adjacent sequences: A226610 A226611 A226612 * A226614 A226615 A226616


KEYWORD

nonn


AUTHOR

Geoffrey H. Morley, Jun 13 2013


STATUS

approved



