A226625 - OEIS

%I #13 Sep 05 2013 07:56:33

%S 1,3,11,4,6,6,17,19,19,19,19,19,19,19,19,34,12,9,5,22,22,22,12,17,17,

%T 17,69,7,7,7,18,44,22,38,38,38,38,38,22,22,33,33,22,11,11,22,11,11,11,

%U 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,48,12

%N Irregular array read by rows. a(n) is the length of the primitive Collatz-like 3x-k cycle associated with A226623(n).

%C Conjecture: Every cycle with the same value of k (k>1) has the same proportion of odd and even elements. Thus if n>1 then A226626(n)/A226625(n) has the same value for each m where A226628(n) <= m < A226628(n+1).

%H Geoffrey H. Morley, <a href="/A226625/b226625.txt">Rows 1..280 of array, flattened</a>

%e The irregular array starts:

%e (k=1)  1, 3, 11;

%e (k=11) 4;

%e (k=17) 6, 6;

%e (k=19) 17;

%e a(4)=4 is the length of the 3x-11 cycle {19,23,29,38} associated with A226623(4)=19.

%Y Row n begins with a(A226628(n)) and has length A226629(n). k=A226630(n)

%Y The cycle associated with a(n) has A226626(n) odd elements of which A226624(n) is the largest.

%Y Cf. A226609, A226627, A226631, A226686, A226687, A226688.

%K nonn,tabf

%O 1,2

%A _Geoffrey H. Morley_, Jun 13 2013