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 A050299 Numbers n such that ((n-1)! + 1)/n is prime. 9
 1, 5, 7, 11, 29, 773, 1321, 2621 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Except for the first term, all terms are primes because for n > 1, n divides (n-1)! + 1 iff n is prime. There are no other terms up to 6550 and the corresponding next prime has more than 22150 digits. No more terms below 30941. LINKS Mike Oakes, posting to Number Theory List, Aug 20 2003 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. Javier Soria, posting to Number Theory List, Apr 08 2003 FORMULA ((a(n)-1)! + 1)/a(n) = A122696(n) = A007619(A000720(A050299(n))) for n > 1. - Jonathan Sondow, Aug 07 2011 a(n) = prime(A225906(n-1)) for n > 1. - Jonathan Sondow, May 20 2013 EXAMPLE 7 is in the sequence because (6!+1)/7=103 is prime. MATHEMATICA v={1}; Do[If[PrimeQ[((Prime[n]-1)!+1)/Prime[n]], v=Append[v, Prime[n]]; Print[v]], {n, 845}] PROG (PARI) is(n)=((n-1)!+1)%n==0 && isprime(((n-1)!+1)/n) \\ Anders Hellström, Nov 22 2015 CROSSREFS Sequence in context: A330775 A031134 A144231 * A092029 A259564 A308764 Adjacent sequences:  A050296 A050297 A050298 * A050300 A050301 A050302 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 09 2003 EXTENSIONS 1321 and 2621 from Mike Oakes, Aug 20 2003 Additional comments from Farideh Firoozbakht, Mar 19 2004 STATUS approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)