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 1-5 of 5 results.

A357001 a(n) = A002729(n) - A357000(n) - 1.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 43, 0, 12, 0, 0, 0, 0, 0, 1954, 8, 0, 342, 0, 0, 0, 0
Offset: 1

Views

Author

Pontus von Brömssen, Sep 08 2022

Keywords

Crossrefs

Cf. A002729, A357000, A357002.

Extensions

a(30)-a(31) (using data in A002729 and A357000) from Pontus von Brömssen, Jun 28 2023

A137706 Smallest number at which a new Haar graph is encountered.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 16, 17, 19, 23, 31, 32, 33, 34, 35, 36, 37, 39, 42, 43, 45, 47, 63, 64, 65, 67, 69, 71, 75, 79, 95, 127, 128, 129, 130, 131, 133, 135, 136, 137, 138, 139, 141, 143, 151, 153, 155, 159, 170, 171, 175, 187, 191, 255, 256, 257, 259, 260
Offset: 1

Views

Author

Eric W. Weisstein, Feb 07 2008

Keywords

Examples

			Haar(5) and Haar(6) are both isomorphic to the 6-cycle graph, so 5 appears in the sequence but 6 does not.

Links

Crossrefs

Cf. A272919 (numbers that uniquely index a Haar graph), A357000.

Extensions

Name clarified by Eric W. Weisstein, Aug 19 2017

A357004 Smallest k for which the cyclic Haar graphs with indices k and n are isomorphic.

Original entry on oeis.org

1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 11, 9, 11, 11, 15, 16, 17, 17, 19, 17, 19, 19, 23, 17, 19, 19, 23, 19, 23, 23, 31, 32, 33, 34, 35, 36, 37, 37, 39, 34, 37, 42, 43, 37, 45, 43, 47, 33, 35, 37, 39, 37, 43, 45, 47, 35, 39, 43, 47, 39, 47, 47, 63, 64, 65, 65, 67, 65
Offset: 1

Views

Author

Pontus von Brömssen, Sep 08 2022

Keywords

Comments

The fixed points are the terms of A137706.
The number of fixed points n in the interval 2^(m-1) <= n < 2^m equals A357000(m).

Links

Crossrefs

Cf. A137706 (fixed points; or ordered list of distinct terms), A163382, A272919 (terms that occur only once), A357000, A357005.

Formula

a(a(n)) = a(n).
a(n) = A357005(n) for n <= 146, but a(147) = 141 < 147 = A357005(147).
a(n) <= A357005(n) <= A163382(n).

A357002 Numbers k such that A357001(k) > 0.

Original entry on oeis.org

8, 16, 18, 24, 25, 27
Offset: 1

Views

Author

Pontus von Brömssen, Sep 08 2022

Keywords

Comments

9*m is a term for all m >= 2 (Hladnik, Marušič, and Pisanski, 2002).

Links

  • Milan Hladnik, Dragan Marušič, and Tomaž Pisanski, Cyclic Haar graphs, Discrete Mathematics 244 (2002), 137-152.

Crossrefs

Cf. A357000, A357001.

A357003 Number of Hamiltonian cycles in the cyclic Haar graph with index n.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 6, 0, 1, 0, 6, 1, 6, 6, 72, 0, 1, 1, 8, 1, 8, 8, 156, 1, 8, 8, 156, 8, 156, 156, 1440, 0, 1, 0, 8, 0, 12, 12, 335, 0, 12, 0, 300, 12, 352, 300, 4800, 1, 8, 12, 335, 12, 300, 352, 4800, 8, 335, 300, 4800, 335, 4800, 4800, 43200, 0, 1, 1, 10, 1
Offset: 1

Views

Author

Pontus von Brömssen, Sep 08 2022

Keywords

Comments

a(n) > 0 for all odd n >= 3 (Hladnik, Marušič, and Pisanski, 2002).

Links

Crossrefs

Cf. A010796, A291165, A357000, A357004.

Formula

a(2^k-1) = A010796(k-1) for k >= 2.
a(A291165(n)) = 0.
a(n) = a(A357004(n)).
Showing 1-5 of 5 results.

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

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