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 1-2 of 2 results.

A182540 Number of ways of arranging the numbers 1 through n on a circle so that no sum of two adjacent numbers is prime, up to rotations and reflections.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 6, 44, 208, 912, 8016, 61952, 671248, 8160620, 87412258, 888954284, 12156253488, 180955852060, 2907927356451, 50317255621843, 802326797235038, 12251146829850324, 233309934271940028, 4243527581615332664, 79533825261873435894, 1602629887788636447221, 30450585799991840921483, 622433536382831426225696, 14891218890120375419560713, 344515231090957672408413959
Offset: 1

Views

Author

Jens Voß, May 04 2012

Keywords

Examples

			If n < 6, then in every arrangement of the numbers 1 through n on a circle, there are two adjacent numbers adding up to a prime. For n = 6, the only arrangement without a prime sum is (1, 3, 6, 2, 4, 5).

Crossrefs

Cf. A051252, A073452, A191374

Extensions

a(15)-a(17) from Alois P. Heinz, May 04 2012
a(18) from R. H. Hardin, May 07 2012
a(19)-a(30) from Max Alekseyev, Aug 19 2013

A191798 Number of essentially different ways of arranging numbers 1 through 2*n around a circle so that the sums of each pair of adjacent numbers are neither all prime nor all composite.

Original entry on oeis.org

0, 2, 58, 2474, 180480, 19895936, 3105348340, 652948189204, 177662757810868, 60772232945639507, 25533219938917963508, 12921764841857675170314, 7754002391777621430686566
Offset: 1

Views

Author

Bennett Gardiner, Jun 16 2011

Keywords

Comments

Finding a pattern, recurrence relation or explicit formula for this sequence would allow us to find terms in A191374 using terms from A051252, or vice versa.

Examples

			a(2) = 2 since the arrangements 1,3,2,4 and 1,3,4,2 both satisfy the condition.

Crossrefs

Cf. A051252, A191374.

Formula

For n>1, a(n) = (2*n-1)!/2 - A051252(n) - A191374(n).

Extensions

a(7) corrected, a(8)-a(13) added by Max Alekseyev, Aug 19 2013
Showing 1-2 of 2 results.

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

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