A226679 -id:A226679 - cp's OEIS frontend

A226680 Integer k associated with the record-breaking number A226679(n) of primitive Collatz-like 3x-k cycles.

Original entry on oeis.org

1, 23, 139, 311, 3299, 7153, 185357

Offset: 1

Geoffrey H. Morley, Jun 15 2013

a(8)>315187.

Cf. A226664.

A226629 a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k=A226630(n).

Original entry on oeis.org

3, 1, 2, 1, 8, 1, 1, 1, 1, 3, 1, 1, 2, 1, 3, 1, 2, 5, 35, 2, 1, 2, 1, 6, 9, 136, 1, 1, 4, 2, 1, 1, 16, 3, 8, 8, 1, 9, 1, 2, 1, 16, 7, 9, 1, 1, 1, 26, 21, 13, 3, 4, 3, 2, 2, 38, 4, 2, 29, 3, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 8, 8, 1, 34, 33, 3, 1, 3, 1, 1, 1, 96, 4

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..600

a(n) is the number of terms in the n-th row of A226623 to A226627.

Cf. A226613, A226679.

a(n) = A226628(n+1) - A226628(n).

A226663 Conjectured record-breaking numbers, for ascending positive integers k, of primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

Original entry on oeis.org

1, 5, 9, 19, 20, 23, 52, 53, 97, 142, 534, 944, 950, 3806, 4782

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, where k is odd.
For primitive cycles, GCD(k,6)=1.

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).
E. G. Belaga and M. Mignotte, Walking Cautiously into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly, Fourth Colloquium on Mathematics and Computer Science, DMTCS proc. AG. (2006), 249-260.
E. G. Belaga and M. Mignotte, The Collatz Problem and Its Generalizations: Experimental Data. Table 1. Primitive Cycles of (3n+d)-mappings, Preprint math. 2006/15, Univ. Louis Pasteur, Strasbourg (2006).

k = A226664(n).

Cf. A226613, A226679.

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A226680 Integer k associated with the record-breaking number A226679(n) of primitive Collatz-like 3x-k cycles.

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A226629 a(n) is the conjectured number of primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k=A226630(n).

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A226663 Conjectured record-breaking numbers, for ascending positive integers k, of primitive cycles of positive integers under iteration by the Collatz-like 3x+k function.

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Author

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