A226677 - OEIS

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 #4 Jul 06 2013 17:19:39

%S 1,1,11,17,115,31,1,29,1417,371,19,23,8977,77,431,2465,2069,3299,193,

%T 451,139,25,5233,131,1739,10993,3037,121,7061,11329,9479,145,2425,

%U 46199,1871,217,3551,26183,14083,26281,7237,605,181,113,3299,11431,119773,2465

%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="/A226677/b226677.txt">Table of n, a(n) for n = 1..60</a>

%Y Cf. A226626, A226661, A226676.

%K nonn

%O 1,3

%A _Geoffrey H. Morley_, Jul 05 2013