cp's OEIS Frontend

A226617 Smallest positive integer k (or 0 if no such k) with a primitive cycle of positive integers, n of which are odd including 1, under iteration by the Collatz-like 3x+k function.

%I A226617 #4 Jul 04 2013 21:11:49
%S A226617 1,11,43,55,643,97,673,41,1843,329,59,113,5603,289,6505,77,407,127,
%T A226617 499,79,865,749
%N A226617 Smallest positive integer k (or 0 if no such k) with a primitive cycle of positive integers, n of which are odd including 1, under iteration by the Collatz-like 3x+k function.
%C A226617 A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.
%C A226617 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 A226617 For primitive cycles, GCD(k,6)=1.
%C A226617 Conjecture: a(n)>0 for all n.
%e A226617 The cycle associated with a(1)=1 is {1,2}, with a(2)=11 is {1,7,16,8,4,2}, and with a(3)=43 is {1,23,56,28,14,7,32,16,8,4,2}.
%Y A226617 Cf. A226607, A226610, A226616.
%K A226617 nonn
%O A226617 1,2
%A A226617 _Geoffrey H. Morley_, Jul 03 2013