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 1-3 of 3 results.

A226620 Irregular array read by rows in which a(n) is the number of odd elements in each primitive '3x+k' cycle associated with A226619(n).

Original entry on oeis.org

1, 0, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 2, 3, 2, 1, 6, 5, 2, 4, 3, 2, 1, 7, 6, 5, 4, 4, 4, 3, 2, 1, 8, 7, 6, 6, 3, 5, 4, 3, 2, 1, 9, 8, 7, 8, 6, 5, 2, 2, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 7, 5, 3, 5, 4, 5, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 9, 8, 8, 8, 8, 4, 4, 7
Offset: 1

Views

Author

Geoffrey H. Morley, Jul 02 2013

Keywords

Comments

The terms in row n are associated with cycles of length n (see A226619).

Examples

			The irregular array starts:
1, 0;
1;
2, 1;
3, 2, 1;
4, 3, 2, 1;
5, 4, 2, 3, 2, 1; ...

Links

Crossrefs

Cf. A226621.

A226621 Irregular array read by rows in which a(n) is the number of primitive '3x+k' cycles associated with A226619(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 3, 1, 1, 1, 3, 1, 5, 5, 2, 1, 1, 3, 7, 1, 2, 5, 7, 3, 1, 1, 4, 8, 1, 1, 14, 14, 8, 4, 1, 1, 3, 12, 1, 6, 2, 1, 1, 14, 23, 20, 12, 2, 1, 1, 5, 15, 29, 1, 1, 1, 2, 5, 5, 42, 34, 25, 14, 5, 1, 1, 5, 16, 28, 2, 9, 1, 1, 1
Offset: 1

Views

Author

Geoffrey H. Morley, Jul 02 2013

Keywords

Comments

The terms in row n are associated with cycles of length n (see A226619).

Examples

			The irregular array starts:
1, 1;
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 2, 1, 3, 1, 1; ...

Links

Crossrefs

Cf. A226620.

A226618 Irregular array read by rows in which row n lists the positive integers k in ascending order for which 1 is in a primitive cycle of n positive integers under iteration by the Collatz-like 3x+k function.

Original entry on oeis.org

1, 5, 13, 29, 11, 61, 17, 125, 253, 509, 145, 203, 1021, 43, 2045, 55, 4093, 355, 1169, 8189, 137, 3275, 16381, 1129, 32765, 1007, 5957, 9361, 65533, 131069, 97, 52427, 262141, 643, 74897, 524285, 41, 1048573, 553, 28727, 110375, 2097149, 281, 673, 2075, 9731, 34663
Offset: 1

Views

Author

Geoffrey H. Morley, Jul 02 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, where k is odd.
For primitive cycles, GCD(k,6)=1.

Examples

			The irregular array starts:
1;
5;
13;
29;
11, 61;
17, 125; ...
Row 1 is empty.

Links

Crossrefs

The first element in row n is A226616(n), and the last is A036563(n) = 2^n-3.
Cf. A226609, A226619.
Showing 1-3 of 3 results.

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

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