A163079 Primes p such that p$ + 1 is also prime. Here '$' denotes the swinging factorial function (A056040).

2, 3, 5, 31, 67, 139, 631, 9743, 16253, 17977, 27901, 37589

Offset: 1

Author

Peter Luschny, Jul 21 2009

Keywords

• nonn
• more

Comments

a(n) are the primes in A163077.

Examples

			5 is prime and 5$ + 1 = 30 + 1 = 31 is prime, so 5 is in the sequence.
		

Links

• Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
• Peter Luschny, Swinging Primes.

Crossrefs

Cf. A002981, A062363, A093804, A163077.

Cf. A056040. - Robert G. Wilson v, Aug 09 2010

Programs

Maple

a := proc(n) select(isprime,select(k -> isprime(A056040(k)+1),[$0..n])) end:

Mathematica

f[n_] := 2^(n - Mod[n, 2])*Product[k^((-1)^(k + 1)), {k, n}]; p = 2; lst = {}; While[p < 38000, a = f@p + 1; If[ PrimeQ@a, AppendTo[ lst, p]; Print@p]; p = NextPrime@p]; lst (* Robert G. Wilson v, Aug 08 2010 *)

PARI

is(k) = isprime(k) && ispseudoprime(1+k!/(k\2)!^2); \\ Jinyuan Wang, Mar 22 2020

Extensions

a(8)-a(12) from Robert G. Wilson v, Aug 08 2010