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 A118812 #30 Sep 06 2025 22:26:17
%S A118812 2,23,87178286161,403291461126605629356979201,
%T A118812 5502622159812088949850305428800254867109635014075023360001
%N A118812 Primes of the form (2*n)! - n! + 1.
%C A118812 a(6) is a 41025-digit prime corresponding to n = 5666, and a(7) is a 288639-digit prime corresponding to n = 32918. See A237443 for additional values of n. - _Kellen Shenton_, Dec 21 2024
%C A118812 Primes in sequence A237580 = n -> (2n)! - n! + 1, i.e., the terms of that sequence which coincide with A237579(n) = least prime factor of (2n)! - n! + 1. - _M. F. Hasler_, Feb 09 2014
%D A118812 G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 159.
%F A118812 A118812 = A237580 o A237443 = A237579 o A237443. - _M. F. Hasler_, Feb 09 2014
%e A118812 For n=2, (2*2)! - 2! + 1 = 24 - 2 + 1 = 23, which is prime.
%p A118812 PFACT:=proc(N) local i,r; for i from 1 by 1 to N do r:=(2*i)!-i!+1; if isprime(r) then print(i); fi; od; end: PFACT(100);
%t A118812 Select[Table[(2n)!-n!+1,{n,30}],PrimeQ] (* _Harvey P. Dale_, May 05 2018 *)
%o A118812 (PARI) for(n=1,999,ispseudoprime(p=(2*n)!-n!+1)&&print1(p",")) \\ _M. F. Hasler_, Feb 09 2014
%Y A118812 Cf. A237443 (corresponding values of n).
%K A118812 nonn,changed
%O A118812 1,1
%A A118812 _Paolo P. Lava_ and _Giorgio Balzarotti_, May 23 2006