A226618 - OEIS

%I #4 Jul 02 2013 23:57:04

%S 1,5,13,29,11,61,17,125,253,509,145,203,1021,43,2045,55,4093,355,1169,

%T 8189,137,3275,16381,1129,32765,1007,5957,9361,65533,131069,97,52427,

%U 262141,643,74897,524285,41,1048573,553,28727,110375,2097149,281,673,2075,9731,34663

%N Irregular array read by rows in which row n lists the positive integers k in ascending order for which 1 is in a primitive cycle of n positive integers 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.

%H Geoffrey H. Morley, <a href="/A226618/b226618.txt">Rows 2..26 of array, flattened</a>

%e The irregular array starts:

%e 1;

%e 5;

%e 13;

%e 29;

%e 11, 61;

%e 17, 125; ...

%e Row 1 is empty.

%Y The first element in row n is A226616(n), and the last is A036563(n) = 2^n-3.

%Y Cf. A226609, A226619.

%K nonn,tabf

%O 1,2

%A _Geoffrey H. Morley_, Jul 02 2013