

A122696


Primes of the form ((n1)! + 1)/n.


4




OFFSET

1,1


COMMENTS

A163212, Wilson quotients (A007619: ((p1)!+1)/p) which are primes, is a subsequence. Corresponding numbers n such that ((n1)! + 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.
J. Sondow, Lerch Quotients, Lerch Primes, FermatWilson Quotients, and the WieferichnonWilson Primes 2, 3, 14771, in Proceedings of CANT 2011, arXiv:1110.3113 [math.NT], 20112012.
J. Sondow, Lerch Quotients, Lerch Primes, FermatWilson Quotients, and the WieferichnonWilson Primes 2, 3, 14771, Combinatorial and Additive Number Theory, CANT 2011 and 2012, Springer Proc. in Math. & Stat., vol. 101 (2014), pp. 243255.


FORMULA

a(n) = A163212(n1) = (((A050299(n)1)! + 1)/A050299(n).  Jonathan Sondow, May 19 2013


PROG

(PARI) is(n)=isprime(((n1)!+1)/n) \\ Anders HellstrÃ¶m, Nov 22 2015 \\ This program actually produces A050299  Michel Marcus, Aug 02 2016
(PARI) for(n=1, 1e2, if(((n1)!+1)%n==0 && isprime(k=((n1)!+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



