A226669 -id:A226669 - cp's OEIS frontend

A226608 Irregular array read by rows. a(n) is the largest element in the primitive Collatz-like 3x+k cycle associated with A226607(n).

1, 1, 49, 37, 2773, 3397, 11, 7, 79, 1, 1853, 1121, 797, 665, 905, 653, 761, 557, 5, 181, 35, 19, 11, 1651, 137, 41, 1, 121, 2277097, 1051393, 131, 127, 79, 89, 53, 65, 157, 23, 43, 643, 331, 223, 211, 259, 175, 1409, 757, 71, 19, 827, 139, 1399, 775, 751, 967, 559, 571

Offset: 1

Geoffrey H. Morley, Jun 13 2013

			The irregular array starts:
(k=1)  1;
(k=5)  1, 49, 37, 2772, 3397;
(k=7)  11;
(k=11) 7, 79;
a(3)=49 is the largest element in the 3x+5 cycle {19,31,49,76,38} associated with A226607(3)=19.

Geoffrey H. Morley, Rows 1..2032 of array, flattened

Row n begins with a(A226612(n)) and has length A226613(n).
The cycle associated with a(n) has length A226609(n) and A226610(n) odd elements.
Cf. A226611, A226624, A226667-A226669.

A226667 Conjectured record-breaking values, for ascending positive integers k, of the maximal element of the primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

Original entry on oeis.org

1, 3397, 2277097, 106035623, 128946539, 153247321, 885327131, 6372904817, 52894692341, 95712964765, 301829916841, 1846456176103, 2697688935023, 10281192195005, 10556691785131, 13239192635131

Offset: 1

Geoffrey H. Morley, Jun 15 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 = A226668(n). The smallest integer in the T_k cycle associated with a(n) is A226669(n).

Cf. A226608, A226683.

A226685 Minimal element in the primitive 3x-k cycle with the conjectured record-breaking maximal element A226683(n).

Original entry on oeis.org

17, 65, 115, 2963, 1085, 7471, 21239, 6329, 436099, 4476457, 1104989, 21111517, 64112905

Offset: 1

Geoffrey H. Morley, Jun 15 2013

nonn

k = A226684(n).

Cf. A226669.

A226668 Integer k associated with the conjectured record-breaking maximal element A226667(n) of primitive Collatz-like 3x+k cycles.

Original entry on oeis.org

1, 5, 29, 343, 439, 3437, 3787, 3949, 13033, 28493, 30809, 42887, 178459, 184861, 215663, 227063

Offset: 1

Geoffrey H. Morley, Jun 15 2013

nonn

Cf. A226669, A226684.

cp's OEIS Frontend

A226608 Irregular array read by rows. a(n) is the largest element in the primitive Collatz-like 3x+k cycle associated with A226607(n).

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A226667 Conjectured record-breaking values, for ascending positive integers k, of the maximal element of the primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

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A226685 Minimal element in the primitive 3x-k cycle with the conjectured record-breaking maximal element A226683(n).

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A226668 Integer k associated with the conjectured record-breaking maximal element A226667(n) of primitive Collatz-like 3x+k cycles.

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