A226660 -id:A226660 - cp's OEIS frontend

A226661 Smallest positive integer k (or 0 if no such k) with a primitive cycle of positive integers, exactly n of which are odd, under iteration by the Collatz-like 3x+k function.

1, 7, 5, 25, 13, 59, 47, 11, 29, 145, 59, 31, 115, 79, 13, 47, 5, 17, 125, 79, 263, 49, 169, 91, 191, 23, 601, 323, 193, 109, 311, 73, 149, 265, 571, 95, 491, 697, 695, 137, 29, 119, 383, 575, 283, 121, 263, 233, 163, 193, 283, 479, 107, 203, 437, 85, 491, 349

Offset: 1

Geoffrey H. Morley, Jul 05 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, where k is odd.
For primitive cycles, GCD(k,6)=1.
Conjecture: a(n)>0 for all n.

Geoffrey H. Morley, Table of n, a(n) for n = 1..2520

Cf. A226610, A226660, A226677.

A226676 Smallest positive integer k (or 0 if no such k) with a primitive cycle of n positive integers under iteration by the Collatz-like 3x-k function.

Original entry on oeis.org

1, 0, 1, 11, 49, 17, 115, 473, 31, 791, 1, 29, 11491, 371, 641, 2167, 19, 119, 23, 3211, 106537, 77, 431, 2465, 2069, 5575

Offset: 1

Geoffrey H. Morley, Jul 05 2013

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, where k is odd,
For primitive cycles, GCD(k,6)=1.
Conjecture: For n>2, a(n)>0.

Cf. A226625, A226660, A226677.

cp's OEIS Frontend

A226661 Smallest positive integer k (or 0 if no such k) with a primitive cycle of positive integers, exactly n of which are odd, under iteration by the Collatz-like 3x+k function.

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