A226689 -id:A226689 - cp's OEIS frontend

A226626 Irregular array read by rows. a(n) is the number of odd elements in the primitive Collatz-like 3x-k cycle associated with A226623(n).

1, 2, 7, 3, 4, 4, 11, 12, 12, 12, 12, 12, 12, 12, 12, 22, 8, 6, 4, 14, 14, 14, 8, 11, 11, 11, 44, 5, 5, 5, 12, 28, 14, 24, 24, 24, 24, 24, 14, 14, 21, 21, 14, 7, 7, 14, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 32, 8

Offset: 1

Geoffrey H. Morley, Jun 13 2013

			The irregular array starts:
(k=1)  1, 2, 7;
(k=11) 3;
(k=17) 4, 4;
(k=19) 11;
a(4)=3 is the number of odd elements in the 3x-11 cycle {19,23,29,38} associated with A226623(4)=19

Geoffrey H. Morley, Rows 1..280 of array, flattened

Row n begins with a(A226628(n)) and has length A226629(n). k=A226630(n).
The cycle associated with a(n) has length A226625(n) and its largest element is A226624(n).
Cf. A226610, A226627, A226632, A226689.

A226673 Conjectured record-breaking numbers of odd elements, for ascending positive integers k, in primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

Original entry on oeis.org

1, 17, 18, 26, 41, 56, 74, 80, 89, 115, 126, 142, 215, 220, 256, 311, 387, 1000, 1136, 1146, 2253, 2292, 2590, 2937, 4971, 5326, 7157, 8294, 9920, 18862, 20429, 24842, 31913

Offset: 1

Geoffrey H. Morley, Jun 19 2013

nonn

A cycle is called primitive if its elements are not a common multiple of the elements of another cycle.
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.
For primitive cycles, GCD(k,6)=1.

k = A226674(n). The smallest integer in the T_k cycle associated with a(n) is A226675(n).

Cf. A226610, A226689.

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A226626 Irregular array read by rows. a(n) is the number of odd elements in the primitive Collatz-like 3x-k cycle associated with A226623(n).

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A226673 Conjectured record-breaking numbers of odd elements, for ascending positive integers k, in primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

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