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A226661 Smallest positive integer k (or 0 if no such k) with a primitive cycle of positive integers, exactly n of which are odd, under iteration by the Collatz-like 3x+k function.

%I A226661 #4 Jul 06 2013 17:18:58
%S A226661 1,7,5,25,13,59,47,11,29,145,59,31,115,79,13,47,5,17,125,79,263,49,
%T A226661 169,91,191,23,601,323,193,109,311,73,149,265,571,95,491,697,695,137,
%U A226661 29,119,383,575,283,121,263,233,163,193,283,479,107,203,437,85,491,349
%N A226661 Smallest positive integer k (or 0 if no such k) with a primitive cycle of positive integers, exactly n of which are odd, under iteration by the Collatz-like 3x+k function.
%C A226661 A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.
%C A226661 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 A226661 For primitive cycles, GCD(k,6)=1.
%C A226661 Conjecture: a(n)>0 for all n.
%H A226661 Geoffrey H. Morley, <a href="/A226661/b226661.txt">Table of n, a(n) for n = 1..2520</a>
%Y A226661 Cf. A226610, A226660, A226677.
%K A226661 nonn
%O A226661 1,2
%A A226661 _Geoffrey H. Morley_, Jul 05 2013