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A226613 a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x+k function, where n=floor(k/3)+1.

%I A226613 #13 Jul 02 2013 13:21:48
%S A226613 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,
%T A226613 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,
%U A226613 1,4,1,3,2,1,2,1,8,19,3,4,2,2,6,2,3,3,7,3
%N A226613 a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x+k function, where n=floor(k/3)+1.
%C A226613 A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.
%C A226613 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.
%C A226613 For primitive cycles, GCD(k,6)=1.
%H A226613 Geoffrey H. Morley, <a href="/A226613/b226613.txt">Table of n, a(n) for n = 1..6667</a>
%H A226613 E. G. Belaga and M. Mignotte, <a href="http://hal.archives-ouvertes.fr/hal-00129656">Cyclic Structure of Dynamical Systems Associated with 3x+d Extensions of Collatz Problem</a>, Preprint math. 2000/17, Univ. Louis Pasteur, Strasbourg (2000). [Table 1 on page 19 gives a(1) to a(500).]
%F A226613 a(n) = A226612(n+1) - A226612(n).
%Y A226613 a(n) is the number of terms in the n-th row of A226607 to A226611.
%Y A226613 Cf. A226629, A226663.
%K A226613 nonn
%O A226613 1,2
%A A226613 _Geoffrey H. Morley_, Jun 13 2013