A163075 Primes of the form k$ + 1. Here '$' denotes the swinging factorial function (A056040).

2, 3, 7, 31, 71, 631, 3433, 51481, 2704157, 280816201, 4808643121, 35345263801, 2104098963721, 94684453367401, 1580132580471901, 483701705079089804581, 6892620648693261354601, 410795449442059149332177041, 2522283613639104833370312431401

Offset: 1

Author

Peter Luschny, Jul 21 2009

Keywords

• nonn

Examples

			Since 3$ = 4$ = 6 the prime 7 is listed, however only once.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..50
• Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
• Peter Luschny, Swinging Primes.

Crossrefs

Cf. A056040, A088332, A163077 (arguments k), A163074, A163076.

Programs

Maple

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

Mathematica

Reap[Do[f = n!/Quotient[n, 2]!^2; If[PrimeQ[p = f + 1], Sow[p]], {n, 1, 70}]][[2, 1]] // Union (* Jean-François Alcover, Jun 28 2013 *)

Extensions

More terms from Jinyuan Wang, Mar 22 2020