A163074 Swinging primes: primes which are within 1 of a swinging factorial (A056040).

2, 3, 5, 7, 19, 29, 31, 71, 139, 251, 631, 3433, 12011, 48619, 51479, 51481, 2704157, 155117519, 280816201, 4808643121, 35345263801, 81676217699, 1378465288199, 2104098963721, 5651707681619, 94684453367401, 386971244197199, 1580132580471899, 1580132580471901

Offset: 1

Author

Peter Luschny, Jul 21 2009

Keywords

• nonn

Comments

Union of A163075 and A163076.

Examples

			3$ + 1 = 7 is prime, so 7 is in the sequence. (Here '$' denotes the swinging factorial function.)
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..103
• Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
• Peter Luschny, Swinging Primes.

Crossrefs

Cf. A088054, A163075, A163076.

Programs

Maple

# Seq with arguments <= n:
a := proc(n) select(isprime,map(x -> A056040(x)+1,[$1..n]));
select(isprime,map(x -> A056040(x)-1,[$1..n]));
sort(convert(convert(%%,set) union convert(%,set),list)) end:

Mathematica

Reap[Do[f = n!/Quotient[n, 2]!^2; If[PrimeQ[p = f - 1], Sow[p]]; If[PrimeQ[p = f + 1], Sow[p]], {n, 1, 45}]][[2, 1]] // Union (* Jean-François Alcover, Jun 28 2013 *)

Extensions

More terms from Jinyuan Wang, Mar 22 2020