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).

1, 5, 17, 19, 65, 73, 115, 2263, 2359, 2743, 2963, 3091, 3415, 3743, 4819, 113, 109, 95, 65, 989, 1153, 1165, 293, 511, 505, 625, 769, 211, 227, 251, 311, 1085, 2089, 7471, 10883, 13963, 15875, 16099, 1291, 1355, 1367, 1495, 1931, 2059, 2123, 2203, 2219, 2251

Offset: 1

Author

Geoffrey H. Morley, Jun 13 2013

Keywords

• nonn
• tabf

Comments

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.

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.

Examples

			The irregular array starts:
(k=1)  1, 5, 17;
(k=11) 19;
(k=17) 65, 73;
(k=19) 115;
a(4)=19 is the smallest number in the 3x-11 cycle {19,23,29,38}.
		

Links

• Geoffrey H. Morley, Rows 1..280 of array, flattened
• J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta Arith. 56 (1990), 33-53.

Crossrefs

Row n begins with a(A226628(n)) and has length A226629(n).

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

Cf. A226607, A226681, A226682.