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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. 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 (list; graph; refs; listen; history; text; internal format)
 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 n-th 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

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Last modified March 26 22:42 EDT 2019. Contains 321565 sequences. (Running on oeis4.)