A226623 - OEIS

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

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OFFSET

1,2

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.

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.

EXAMPLE

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}.

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.

Sequence in context: A217079 A153320 A171253 * A171255 A304540 A306125

Adjacent sequences: A226620 A226621 A226622 * A226624 A226625 A226626

KEYWORD

nonn,tabf

AUTHOR

Geoffrey H. Morley, Jun 13 2013

STATUS

approved