This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A152413 #18 Feb 16 2025 08:33:09 %S A152413 61,251,479 %N A152413 Generalized Wilson primes of order 17; or primes p such that p^2 divides 16!(p-17)! + 1. %C A152413 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. %C A152413 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). %H A152413 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WilsonPrime.html">Wilson Prime</a> %Y A152413 Cf. A007540, A007619, A079853, A124405, A128666. %K A152413 bref,hard,more,nonn %O A152413 1,1 %A A152413 _Alexander Adamchuk_, Dec 03 2008 %E A152413 Edited by _Max Alekseyev_, Jan 28 2012