This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A152413 Generalized Wilson primes of order 17; or primes p such that p^2 divides 16!(p-17)! + 1. 2
 61, 251, 479 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Wilson's theorem states that (p-1)! == -1 (mod p) for every prime p. Wilson primes are the primes p such that p^2 divides (p-1)! + 1. They are listed in A007540. Wilson's theorem can be expressed in general as (n-1)!(p-n)! == (-1)^n (mod p) for every prime p >= n. Generalized Wilson primes order n are the primes p such that p^2 divides (n-1)!(p-n)! - (-1)^n. Alternatively, prime p=prime(k) is a generalized Wilson prime order n iff A002068(k) == A007619(k) == H(n-1) (mod p), where H(n-1) = A001008(n-1)/A002805(n-1) is (n-1)-st harmonic number. For this sequence (n=17), it reduces to A002068(k) == A007619(k) == 2436559/720720 (mod p). LINKS 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)