A163080 Primes p such that p$ - 1 is also prime. Here '$' denotes the swinging factorial function (A056040).

3, 5, 7, 13, 41, 47, 83, 137, 151, 229, 317, 389, 1063, 2371, 6101, 7873, 13007, 19603

Offset: 1

Author

Peter Luschny, Jul 21 2009

Keywords

• nonn
• more

Comments

a(n) are the primes in A163078.

Examples

			3 is prime and 3$ - 1 = 5 is prime, so 3 is in the sequence.
		

Links

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

Crossrefs

Cf. A056040, A103317, A163079, A163078.

Programs

Maple

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

Mathematica

sf[n_] := n!/Quotient[n, 2]!^2; Select[Prime /@ Range[200], PrimeQ[sf[#] - 1] &] (* Jean-François Alcover, Jun 28 2013 *)

PARI

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

Extensions

a(14)-a(18) from Jinyuan Wang, Mar 22 2020