A226663 -id:A226663 - cp's OEIS frontend

A226664 Integer k associated with the record-breaking number A226663(n) of primitive Collatz-like 3x+k cycles.

Original entry on oeis.org

1, 5, 13, 233, 355, 431, 499, 1319, 1631, 6005, 6487, 14303, 45853, 71515, 186793

Offset: 1

Geoffrey H. Morley, Jun 15 2013

nonn

Cf. A226680.

A226613 a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x+k function, where n=floor(k/3)+1.

Original entry on oeis.org

1, 5, 1, 2, 9, 2, 1, 3, 2, 4, 1, 2, 3, 1, 1, 7, 1, 1, 3, 7, 2, 1, 1, 7, 3, 1, 4, 3, 1, 1, 3, 3, 2, 7, 2, 1, 1, 1, 2, 5, 2, 4, 2, 3, 2, 5, 1, 3, 3, 2, 2, 1, 1, 4, 2, 3, 2, 2, 7, 1, 3, 1, 2, 3, 4, 1, 2, 2, 1, 4, 1, 3, 2, 1, 2, 1, 8, 19, 3, 4, 2, 2, 6, 2, 3, 3, 7, 3

Offset: 1

Geoffrey H. Morley, Jun 13 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.

Geoffrey H. Morley, Table of n, a(n) for n = 1..6667
E. G. Belaga and M. Mignotte, Cyclic Structure of Dynamical Systems Associated with 3x+d Extensions of Collatz Problem, Preprint math. 2000/17, Univ. Louis Pasteur, Strasbourg (2000). [Table 1 on page 19 gives a(1) to a(500).]

a(n) is the number of terms in the n-th row of A226607 to A226611.

Cf. A226629, A226663.

a(n) = A226612(n+1) - A226612(n).

A226679 Record-breaking values, for increasing k = A226630(n), of the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function.

Original entry on oeis.org

3, 8, 35, 136, 171, 2908, 6326

Offset: 1

Geoffrey H. Morley, Jun 15 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.

k = A226680(n).

Cf. A226629, A226663.

Definition clarified by Geoffrey H. Morley, Jun 23 2013

cp's OEIS Frontend

A226664 Integer k associated with the record-breaking number A226663(n) of primitive Collatz-like 3x+k cycles.

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A226613 a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x+k function, where n=floor(k/3)+1.

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A226679 Record-breaking values, for increasing k = A226630(n), of the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function.

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