A226629 - OEIS

%I #15 Sep 05 2013 07:56:47

%S 3,1,2,1,8,1,1,1,1,3,1,1,2,1,3,1,2,5,35,2,1,2,1,6,9,136,1,1,4,2,1,1,

%T 16,3,8,8,1,9,1,2,1,16,7,9,1,1,1,26,21,13,3,4,3,2,2,38,4,2,29,3,1,1,1,

%U 1,1,5,1,3,1,1,8,8,1,34,33,3,1,3,1,1,1,96,4

%N a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k=A226630(n).

%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.

%H Geoffrey H. Morley, <a href="/A226629/b226629.txt">Table of n, a(n) for n = 1..600</a>

%F a(n) = A226628(n+1) - A226628(n).

%Y a(n) is the number of terms in the n-th row of A226623 to A226627.

%Y Cf. A226613, A226679.

%K nonn

%O 1,1

%A _Geoffrey H. Morley_, Jun 13 2013