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

1,1

Comments

a(n) are the primes in A163077.

Links

Table of n, a(n) for n=1..12.

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

Peter Luschny, Swinging Primes.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A002981, A062363, A093804, A163077.

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

Sequence in context: A265807 A106308 A036797 * A109845 A241722 A276043

Adjacent sequences: A163076 A163077 A163078 * A163080 A163081 A163082

Keyword

nonn,more

Author

Peter Luschny, Jul 21 2009

Extensions

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

Status

approved