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 A193447 #32 Sep 17 2018 11:27:16 %S A193447 3,3299,255877,4807626353,1040021719579,100970241446066087, %T A193447 13409937746820630739862069,9507270961010432209186683871, %U A193447 7757618593382991688938927430572972973,12437732976339904486975781548721278876097561,18522993694996570934756402022946152638511627907 %N A193447 a(n) = ((p - 2)! + p - 1)/(p*(p - 1)) where p is the n-th prime. %C A193447 Conjecture: for k >= 7, ((k - 2)! + k - 1)/(k*(k - 1)) is an integer iff k is prime. %C A193447 Proof follows from Wilson's theorem. - _Alois P. Heinz_, Aug 07 2011 %C A193447 Note that a(1) = 1 is also an integer. - _Jianing Song_, Sep 17 2018 %H A193447 Wikipedia, <a href="http://en.wikipedia.org/wiki/Wilson's_theorem">Wilson's theorem</a> %e A193447 a(4) = (5! + 6)/(7*6) = 126/42 = 3. %e A193447 a(5) = (9! + 10)/(11*10) = 362890/110 = 3299. %o A193447 (PARI) a(n) = my(p=prime(n)); ((p-2)!+p-1)/(p*(p-1)) \\ _Jianing Song_, Sep 17 2018 %Y A193447 Cf. A000040, A007619, A066161. %K A193447 nonn %O A193447 4,1 %A A193447 _Alzhekeyev Ascar M_, Jul 26 2011 %E A193447 Name clarified by _Jianing Song_, Sep 17 2018