login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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).
10

%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