A163211 - OEIS

%I #8 May 08 2020 17:44:09

%S 3,23,71,757,30671,1383331,245273927,3362110459,107752663194272623,

%T 5117886516250502670227,

%U 34633371587745726679416744736000996167729085703,114326045625240879227044995173712991937709388241980425799

%N Swinging Wilson quotients (A163210) which are primes.

%C 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

%H G. C. Greubel, <a href="/A163211/b163211.txt">Table of n, a(n) for n = 1..16</a>

%H Peter Luschny, <a href="/A180000/a180000.pdf">Die schwingende Fakultät und Orbitalsysteme</a>, August 2011.

%H Peter Luschny, <a href="http://www.luschny.de/math/primes/SwingingPrimes.html"> Swinging Primes.</a>

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

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

%t 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 *)

%o (PARI) sf(n)=n!/(n\2)!^2

%o forprime(p=2,1e3, t=sf(p-1)\/p; if(isprime(t), print1(t", "))) \\ _Charles R Greathouse IV_, Dec 11 2016

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

%K nonn

%O 1,1

%A _Peter Luschny_, Jul 24 2009