A226633 -id:A226633 - cp's OEIS frontend

A226634 Length of the primitive 3x-k cycle associated with A226633(n).

1, 4, 6, 17, 19, 34, 12, 9, 5, 22, 12, 17, 17, 69, 7, 18, 44, 38, 22, 48, 6, 68, 44, 30, 54, 38, 68, 14, 22, 44, 23, 30, 84, 8, 17, 17, 30, 12, 68, 18, 7, 66, 30, 22, 85, 10, 14, 66, 44, 30, 14, 54, 44, 12, 68, 44, 9, 38, 34, 14, 55, 8, 56, 50, 36, 44, 25, 37

Offset: 1

Geoffrey H. Morley, Jun 14 2013

nonn

Geoffrey H. Morley, Table of n, a(n) for n = 1..600

Cf. A102284.

A226630 Positive integers k with at least one primitive cycle of positive integers under iteration by the 3x-k function.

Original entry on oeis.org

1, 11, 17, 19, 23, 25, 29, 31, 49, 77, 85, 95, 97, 113, 115, 119, 121, 131, 139, 145, 179, 181, 185, 193, 217, 311, 313, 371, 385, 407, 431, 451, 467, 473, 475, 485, 491, 493, 503, 527, 601, 605, 641, 695, 697, 791, 805, 847, 973, 1163, 1219, 1241, 1295, 1417

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. GCD(k,6)=1.

Geoffrey H. Morley, Table of n, a(n) for n = 1..600

Cf. A226633.

A102280 Let k = n-th number == 1 or 5 mod 6 (A007310(n)); consider the generalized 3x+1 map T_k defined by T_k(n) = (3n+k)/2 if n odd, n/2 if n even; then a(n) = smallest positive number m which is in a primitive cycle of T_k.

Original entry on oeis.org

1, 1, 5, 1, 1, 1, 5, 5, 7, 1, 13, 13, 19, 1, 1, 5, 25, 103, 1, 1, 1, 19, 17, 29, 5, 1, 1, 65, 7, 17, 1, 1, 1, 7, 5, 1, 19, 1, 13, 1, 5, 1, 1, 13, 11, 1, 11, 7, 1, 19, 41, 1, 13, 11, 11, 13, 11, 7, 29, 5, 11, 1, 5, 47, 1, 5, 13, 1, 43, 1, 37, 1, 17, 5, 35, 5, 7, 5, 11, 1, 7, 43, 1, 91, 1, 1, 29, 7, 47, 55, 17, 1, 13

Offset: 1

N. J. A. Sloane, Feb 19 2005

nonn

Geoffrey H. Morley, Table of n, a(n) for n = 1..10000
J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta Arith. 56 (1990), 33-53. - See Table 3.1 on page 41.

Cf. A102284, A007310, A226633.

a(12)[k=35] and a(25)[k=73] corrected and more terms added by Geoffrey H. Morley, Mar 14 2013

cp's OEIS Frontend

A226634 Length of the primitive 3x-k cycle associated with A226633(n).

Views

Author

Keywords

Links

Crossrefs

A226630 Positive integers k with at least one primitive cycle of positive integers under iteration by the 3x-k function.

Views

Author

Keywords

Comments

Links

Crossrefs

A102280 Let k = n-th number == 1 or 5 mod 6 (A007310(n)); consider the generalized 3x+1 map T_k defined by T_k(n) = (3n+k)/2 if n odd, n/2 if n even; then a(n) = smallest positive number m which is in a primitive cycle of T_k.

Views

Author

Keywords

Links

Crossrefs

Extensions