A163212 Wilson quotients (A007619) which are primes.

5, 103, 329891, 10513391193507374500051862069

Offset: 1

Author

Peter Luschny, Jul 24 2009

Keywords

• nonn
• more

Comments

a(5) = A007619(137), a(6) = A007619(216), a(7) = A007619(381).

Same as A122696 without its initial term 2. - Jonathan Sondow, May 19 2013

Examples

			The quotient (720+1)/7 = 103 is a Wilson quotient and a prime, so 103 is a member.
		

Links

• Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
• Peter Luschny, Swinging Primes.
• Jonathan Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, in Proceedings of CANT 2011, arXiv:1110.3113 [math.NT], 2011-2012.
• Jonathan Sondow, Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243-255.

Crossrefs

Cf. A050299, A163211, A007619, A122696, A163210, A163213, A163209, A225906.

Programs

Maple

# WQ defined in A163210.
A163212 := n -> select(isprime,WQ(factorial,p->1,n)):

Mathematica

Select[Table[p = Prime[n]; ((p-1)!+1)/p, {n, 1, 15}], PrimeQ] (* Jean-François Alcover, Jun 28 2013 *)

PARI

forprime(p=2, 1e4, a=((p-1)!+1)/p; if(ispseudoprime(a), print1(a, ", "))) \\ Felix Fröhlich, Aug 03 2014

Formula

a(n) = A122696(n+1) = A007619(A225906(n)) = ((A050299(n+1)-1)!+1)/A050299(n+1). - Jonathan Sondow, May 19 2013