A226661 - OEIS

%I #4 Jul 06 2013 17:18:58

%S 1,7,5,25,13,59,47,11,29,145,59,31,115,79,13,47,5,17,125,79,263,49,

%T 169,91,191,23,601,323,193,109,311,73,149,265,571,95,491,697,695,137,

%U 29,119,383,575,283,121,263,233,163,193,283,479,107,203,437,85,491,349

%N 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 A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.

%C 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 For primitive cycles, GCD(k,6)=1.

%C Conjecture: a(n)>0 for all n.

%H Geoffrey H. Morley, <a href="/A226661/b226661.txt">Table of n, a(n) for n = 1..2520</a>

%Y Cf. A226610, A226660, A226677.

%K nonn

%O 1,2

%A _Geoffrey H. Morley_, Jul 05 2013