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 A163212 Wilson quotients (A007619) which are primes. 5
 5, 103, 329891, 10513391193507374500051862069 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011. Peter Luschny, Swinging Primes. J. 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. J. 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. FORMULA a(n) = A122696(n+1) = A007619(A225906(n)) = ((A050299(n+1)-1)!+1)/A050299(n+1). - Jonathan Sondow, May 19 2013 EXAMPLE The quotient (720+1)/7 = 103 is a Wilson quotient and a prime, so 103 is a member. 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 *) PROG (PARI) forprime(p=2, 1e4, a=((p-1)!+1)/p; if(ispseudoprime(a), print1(a, ", "))) \\ Felix Fröhlich, Aug 03 2014 CROSSREFS Cf. A050299, A163211, A007619, A122696, A163210, A163213, A163209, A225906. Sequence in context: A159523 A172116 A007619 * A163154 A165387 A156848 Adjacent sequences:  A163209 A163210 A163211 * A163213 A163214 A163215 KEYWORD nonn AUTHOR Peter Luschny, Jul 24 2009 STATUS approved

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Last modified June 1 11:51 EDT 2020. Contains 334762 sequences. (Running on oeis4.)