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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, 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
Sequence in context: A159523 A172116 A007619 * A163154 A354157 A165387
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 24 2009
STATUS
approved

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)