cp's OEIS Frontend

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

%I A122696 #47 Nov 09 2024 12:11:15
%S A122696 2,5,103,329891,10513391193507374500051862069
%N A122696 Primes of the form ((k-1)! + 1)/k.
%C A122696 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 A122696 Except for a(1) = 2, same as A163212. - _Jonathan Sondow_, May 20 2013
%H A122696 Jonathan 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 A122696 Jonathan 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 A122696 a(n) = A163212(n-1) = ((A050299(n)-1)! + 1)/A050299(n). - _Jonathan Sondow_, May 19 2013
%t A122696 Select[Table[((k-1)!+1)/k,{k,30}],PrimeQ] (* _James C. McMahon_, Nov 09 2024 *)
%o A122696 (PARI) is(n)=isprime(((n-1)!+1)/n) \\ _Anders Hellström_, Nov 22 2015 \\ This program actually produces A050299 - _Michel Marcus_, Aug 02 2016
%o A122696 (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 A122696 A050299 is the main entry for this sequence.
%Y A122696 Cf. A007619, A163212.
%K A122696 nonn
%O A122696 1,1
%A A122696 _Alexander Adamchuk_, Sep 22 2006
%E A122696 The next term is too large to include.
%E A122696 a(4) and first comment corrected by _Gionata Neri_, Aug 02 2016