cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A226672 Smallest positive integer in the primitive Collatz-like 3x+k cycle(s) with the conjectured record-breaking length A226670(n).

Original entry on oeis.org

1, 187, 23, 41, 3811, 235, 7, 1, 899, 11, 7, 5, 13, 35, 25, 5, 19, 13, 13, 1, 23, 17, 23, 5, 7, 25, 13, 29, 11, 23, 31, 161, 13, 5, 1, 67
Offset: 1

Views

Author

Geoffrey H. Morley, Jun 16 2013

Keywords

Crossrefs

k = A226671(n).
Cf. A226688.

A226671 Integer k associated with the conjectured record-breaking length A226670(n) of primitive Collatz-like 3x+k cycles.

Original entry on oeis.org

1, 5, 17, 23, 29, 61, 85, 107, 125, 139, 143, 197, 253, 313, 371, 509, 563, 1135, 1163, 1307, 1699, 3299, 8431, 11491, 16819, 22097, 24917, 49787, 67475, 76733, 99391, 110273, 111611, 144379, 273641, 308219
Offset: 1

Views

Author

Geoffrey H. Morley, Jun 16 2013

Keywords

Crossrefs

Cf. A226672, A226687.

A226609 Irregular array read by rows. a(n) is the length of the primitive Collatz-like 3x+k cycle associated with A226607(n).

Original entry on oeis.org

2, 3, 5, 5, 27, 27, 4, 6, 14, 4, 24, 8, 8, 8, 8, 8, 8, 8, 7, 31, 11, 5, 5, 43, 16, 8, 5, 17, 65, 65, 23, 8, 8, 6, 6, 6, 20, 11, 18, 28, 7, 7, 7, 7, 7, 38, 29, 12, 6, 28, 28, 10, 10, 10, 10, 10, 10, 6, 66, 24, 30, 10, 10, 27, 27, 27, 27, 27, 12, 60, 15, 38
Offset: 1

Views

Author

Geoffrey H. Morley, Jun 13 2013

Keywords

Examples

			The irregular array starts:
(k=1)  2;
(k=5)  3, 5, 5, 27, 27;
(k=7)  4;
(k=11) 6, 14;
a(2)=3 is the length of the 3x+5 cycle {1,4,2} associated with A226607(2)=1.

Links

Crossrefs

Row n begins with a(A226612(n)) and has length A226613(n).
The cycle associated with a(n) has A226610(n) odd elements of which A226608(n) is the largest.
Cf. A226611, A226625, A226670-A226672.

A226686 Conjectured record-breaking lengths, 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

11, 17, 19, 34, 69, 84, 85, 168, 171, 176, 179, 228, 252, 285
Offset: 1

Views

Author

Geoffrey H. Morley, Jun 16 2013

Keywords

Comments

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.

Crossrefs

k = A226687(n). The smallest integer in the T_k cycle(s) associated with a(n) is A226688(n).
Cf. A226625, A226670.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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