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

2, 5, 103, 329891, 10513391193507374500051862069

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

Table of n, a(n) for n=1..5.

Jonathan 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.

Jonathan 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

Mathematica

Select[Table[((k-1)!+1)/k, {k, 30}], PrimeQ] (* James C. McMahon, Nov 09 2024 *)

Prog

(PARI) is(n)=isprime(((n-1)!+1)/n) \\ Anders Hellström, 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