A163077 Numbers k such that k$ + 1 is prime. Here '$' denotes the swinging factorial function (A056040).

0, 1, 2, 3, 4, 5, 8, 9, 14, 15, 24, 27, 31, 38, 44, 45, 49, 67, 76, 92, 99, 119, 124, 133, 136, 139, 144, 168, 171, 185, 265, 291, 332, 368, 428, 501, 631, 680, 689, 696, 765, 789, 890, 1034, 1233, 1384, 1517, 1615, 1634, 1809, 2632, 2762, 3925, 4419, 5108, 5426

Offset: 1

Author

Peter Luschny, Jul 21 2009

Keywords

• nonn

Examples

			0$ + 1 = 1 + 1 = 2 is prime, so 0 is in the sequence.
		

Links

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

Crossrefs

Cf. A002981, A163078, A163079, A163080.

Programs

Maple

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

Mathematica

fQ[n_] := PrimeQ[1 + 2^(n - Mod[n, 2])*Product[k^((-1)^(k + 1)), {k, n}]]; Select[ Range[0, 8660], fQ] (* Robert G. Wilson v, Aug 09 2010 *)

PARI

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

Extensions

a(45)-a(56) from Robert G. Wilson v, Aug 09 2010