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

1,1

Comments

a(n) are the primes in A163078.

Links

Table of n, a(n) for n=1..18.

Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.

Peter Luschny, Swinging Primes.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A056040, A103317, A163079, A163078.

Sequence in context: A075557 A244452 A057187 * A141414 A236464 A064268

Adjacent sequences: A163077 A163078 A163079 * A163081 A163082 A163083

Keyword

nonn,more

Author

Peter Luschny, Jul 21 2009

Extensions

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

Status

approved