A226617 - OEIS

%I #4 Jul 04 2013 21:11:49

%S 1,11,43,55,643,97,673,41,1843,329,59,113,5603,289,6505,77,407,127,

%T 499,79,865,749

%N 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 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.

%e 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 Cf. A226607, A226610, A226616.

%K nonn

%O 1,2

%A _Geoffrey H. Morley_, Jul 03 2013