A163211 Swinging Wilson quotients (A163210) which are primes.

3, 23, 71, 757, 30671, 1383331, 245273927, 3362110459, 107752663194272623, 5117886516250502670227, 34633371587745726679416744736000996167729085703, 114326045625240879227044995173712991937709388241980425799

Offset: 1

Author

Peter Luschny, Jul 24 2009

Keywords

• nonn

Comments

a(14)-a(18) certified prime by Primo 4.2.0. a(17) = A163210(569) = P1239, a(18) = A163210(787) = P1812. - Charles R Greathouse IV, Dec 11 2016

Examples

			The quotient (252+1)/11 = 23 is a swinging Wilson quotient and a prime, so 23 is a member.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..16
• Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
• Peter Luschny, Swinging Primes.

Crossrefs

Cf. A163210, A163213, A163212, A163209, A007619.

Programs

Maple

A163211 := n -> select(isprime,A163210(n));

Mathematica

sf[n_] := n!/Quotient[n, 2]!^2; a[n_] := (p = Prime[n]; (sf[p - 1] + (-1)^Floor[(p + 2)/2])/p); Select[PrimeQ][Table[a[n], {n, 1, 100}]] (* G. C. Greubel, Dec 10 2016 *)

PARI

sf(n)=n!/(n\2)!^2
forprime(p=2,1e3, t=sf(p-1)\/p; if(isprime(t), print1(t", "))) \\ Charles R Greathouse IV, Dec 11 2016