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

1,1

Comments

Union of A163075 and A163076.

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.

Example

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

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 *)

Crossrefs

Cf. A088054, A163075, A163076.

Sequence in context: A025019 A140327 A346167 * A230041 A068803 A184902

Adjacent sequences: A163071 A163072 A163073 * A163075 A163076 A163077

Keyword

nonn

Author

Peter Luschny, Jul 21 2009

Extensions

More terms from Jinyuan Wang, Mar 22 2020

Status

approved