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A226677 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 A226677 #4 Jul 06 2013 17:19:39
%S A226677 1,1,11,17,115,31,1,29,1417,371,19,23,8977,77,431,2465,2069,3299,193,
%T A226677 451,139,25,5233,131,1739,10993,3037,121,7061,11329,9479,145,2425,
%U A226677 46199,1871,217,3551,26183,14083,26281,7237,605,181,113,3299,11431,119773,2465
%N A226677 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 A226677 A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.
%C A226677 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 A226677 For primitive cycles, GCD(k,6)=1.
%C A226677 Conjecture: a(n)>0 for all n.
%H A226677 Geoffrey H. Morley, <a href="/A226677/b226677.txt">Table of n, a(n) for n = 1..60</a>
%Y A226677 Cf. A226626, A226661, A226676.
%K A226677 nonn
%O A226677 1,3
%A A226677 _Geoffrey H. Morley_, Jul 05 2013