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A122696 Primes of the form ((n-1)! + 1)/n. 4

%I

%S 2,5,103,329891,10513391193507374500051862069

%N Primes of the form ((n-1)! + 1)/n.

%C 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.

%C Except for a(1) = 2, same as A163212. - _Jonathan Sondow_, May 20 2013

%H J. Sondow, <a href="http://arxiv.org/abs/1110.3113"> Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771</a>, in Proceedings of CANT 2011, arXiv:1110.3113 [math.NT], 2011-2012.

%H J. Sondow, <a href="http://dx.doi.org/10.1007/978-1-4939-1601-6_17">Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771</a>, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243-255.

%F a(n) = A163212(n-1) = (((A050299(n)-1)! + 1)/A050299(n). - _Jonathan Sondow_, May 19 2013

%o (PARI) is(n)=isprime(((n-1)!+1)/n) \\ _Anders Hellström_, Nov 22 2015 \\ This program actually produces A050299 - _Michel Marcus_, Aug 02 2016

%o (PARI) for(n=1, 1e2, if(((n-1)!+1)%n==0 && isprime(k=((n-1)!+1)/n), print1(k, ", "))) \\ _Altug Alkan_, Nov 22 2015

%Y A050299 is the main entry for this sequence.

%Y Cf. A007619, A163212.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Sep 22 2006

%E The next term is too large to include.

%E a(4) and first comment corrected by _Gionata Neri_, Aug 02 2016

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Last modified June 4 04:39 EDT 2020. Contains 334815 sequences. (Running on oeis4.)