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 A286181 #21 May 04 2017 22:06:41 %S A286181 7841,594278556271608991, %T A286181 4259842839142238791410741595983041626644087433 %N A286181 Lesser of Wilson's pseudo-twin primes: primes p such that p! == 1 (mod q), where q=A151800(p) is the next prime after p, and q-p>2. %C A286181 By Wilson's theorem, p! == 1 (mod p+2) whenever p,p+2 are twin primes. This sequence and A286208 concern consecutive primes p,q satisfying p! = 1 (mod q), where d = q-p > 2. %C A286181 It follows that (d-1)! == 1 (mod q), and so q divides A033312(d-1). %C A286181 Listed terms correspond to d = 12, 30, 76 (cf. A286230). Further terms should have d>=140. %C A286181 Also, primes p=prime(n) such that A275111(n)=1, and (prime(n),prime(n+1)) are not twin primes (i.e., p is not a term of A001359). %e A286181 For a(1)=7841, we have 7841! == 1 (mod 7853), where 7841 and 7853=7841+12 are consecutive primes. Also, 7853 | (12-1)!-1. %Y A286181 Cf. A275111, A286208. %K A286181 bref,nonn,more %O A286181 1,1 %A A286181 _Max Alekseyev_ and _Thomas Ordowski_, May 04 2017