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 A122696 Primes of the form ((n-1)! + 1)/n. 4
 2, 5, 103, 329891, 10513391193507374500051862069 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A163212, Wilson quotients (A007619: ((p-1)!+1)/p) which are primes, is a subsequence. Corresponding numbers n such that ((n-1)! + 1)/n is prime are listed in A050299 = {1, 5, 7, 11, 29, 773, 1321, 2621, ...}. a(6) has 1893 digits. a(7) has 3545 digits. a(8) has 7817 digits. Except for a(1) = 2, same as A163212. - Jonathan Sondow, May 20 2013 LINKS 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) = A163212(n-1) = (((A050299(n)-1)! + 1)/A050299(n). - Jonathan Sondow, May 19 2013 PROG (PARI) is(n)=isprime(((n-1)!+1)/n) \\ Anders HellstrÃ¶m, Nov 22 2015 \\ This program actually produces A050299 - Michel Marcus, Aug 02 2016 (PARI) for(n=1, 1e2, if(((n-1)!+1)%n==0 && isprime(k=((n-1)!+1)/n), print1(k, ", "))) \\ Altug Alkan, Nov 22 2015 CROSSREFS A050299 is the main entry for this sequence. Cf. A007619, A163212. Sequence in context: A215845 A276110 A136106 * A237267 A266284 A215572 Adjacent sequences:  A122693 A122694 A122695 * A122697 A122698 A122699 KEYWORD nonn AUTHOR Alexander Adamchuk, Sep 22 2006 EXTENSIONS The next term is too large to include. a(4) and first comment corrected by Gionata Neri, Aug 02 2016 STATUS approved

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)