

A152413


Generalized Wilson primes of order 17; or primes p such that p^2 divides 16!(p17)! + 1.


2




OFFSET

1,1


COMMENTS

Wilson's theorem states that (p1)! == 1 (mod p) for every prime p. Wilson primes are the primes p such that p^2 divides (p1)! + 1. They are listed in A007540. Wilson's theorem can be expressed in general as (n1)!(pn)! == (1)^n (mod p) for every prime p >= n. Generalized Wilson primes order n are the primes p such that p^2 divides (n1)!(pn)!  (1)^n.
Alternatively, prime p=prime(k) is a generalized Wilson prime order n iff A002068(k) == A007619(k) == H(n1) (mod p), where H(n1) = A001008(n1)/A002805(n1) is (n1)st harmonic number. For this sequence (n=17), it reduces to A002068(k) == A007619(k) == 2436559/720720 (mod p).


LINKS

Table of n, a(n) for n=1..3.
Eric Weisstein's World of Mathematics, Wilson Prime


CROSSREFS

Cf. A007540, A007619, A079853, A124405, A128666.
Sequence in context: A158673 A174333 A158680 * A029815 A142424 A252803
Adjacent sequences: A152410 A152411 A152412 * A152414 A152415 A152416


KEYWORD

bref,hard,more,nonn


AUTHOR

Alexander Adamchuk, Dec 03 2008


EXTENSIONS

Edited by Max Alekseyev, Jan 28 2012


STATUS

approved



