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A226623 Irregular array read by rows in which row n lists the smallest elements, in ascending order, of conjecturally all primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k = A226630(n).

%I A226623 #16 Jul 04 2013 21:12:31
%S A226623 1,5,17,19,65,73,115,2263,2359,2743,2963,3091,3415,3743,4819,113,109,
%T A226623 95,65,989,1153,1165,293,511,505,625,769,211,227,251,311,1085,2089,
%U A226623 7471,10883,13963,15875,16099,1291,1355,1367,1495,1931,2059,2123,2203,2219,2251
%N A226623 Irregular array read by rows in which row n lists the smallest elements, in ascending order, of conjecturally all primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k = A226630(n).
%C A226623 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 A226623 Lagarias (1990) called a T_k cycle primitive if its elements are all relatively prime to k or, equivalently, if its elements are not a common multiple of the elements of another cycle.
%H A226623 Geoffrey H. Morley, <a href="/A226623/b226623.txt">Rows 1..280 of array, flattened</a>
%H A226623 J. C. Lagarias, <a href="http://pldml.icm.edu.pl:80/mathbwn/element/bwmeta1.element.bwnjournal-article-aav56i1p33bwm?q=bwmeta1.element.bwnjournal-number-aa-1990-56-1&amp;qt=CHILDREN-STATELESS">The set of rational cycles for the 3x+1 problem,</a> Acta Arith. 56 (1990), 33-53.
%e A226623 The irregular array starts:
%e A226623 (k=1)  1, 5, 17;
%e A226623 (k=11) 19;
%e A226623 (k=17) 65, 73;
%e A226623 (k=19) 115;
%e A226623 a(4)=19 is the smallest number in the 3x-11 cycle {19,23,29,38}.
%Y A226623 Row n begins with a(A226628(n)) and has length A226629(n).
%Y A226623 The smallest starting value whose trajectory includes a(n) is A226627(n). The cycle associated with a(n) has length A226625(n) and A226626(n) odd elements of which A226624(n) is the largest
%Y A226623 Cf. A226607, A226681, A226682.
%K A226623 nonn,tabf
%O A226623 1,2
%A A226623 _Geoffrey H. Morley_, Jun 13 2013