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.
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
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).
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