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 A083340 #18 Sep 25 2023 05:13:06 %S A083340 6,7,8,12,15,16,17,18,19,28,29,41,45,53,55,61,73 %N A083340 Numbers n such that A020549(n)=(n!)^2+1 is a semiprime. %C A083340 The smaller of the two prime factors is given in A083341. The next candidates for a continuation are 55 and 61. (55!)^2 + 1 is composite with 147 decimal digits and unknown factorization. %C A083340 (55!)^2 + 1 has been factored using ECM into P52*P96 with P52 = A083341(15). (61!)^2 + 1 is composite with 168 decimal digits. - _Hugo Pfoertner_, Jul 13 2019 %C A083340 Using CADO-NFS, (61!)^2 + 1 has been factored into P58*P110 with P58 = A282706(61) in 17 days wall clock time using 56 million CPU seconds. a(18) >= 75. - _Hugo Pfoertner_, Aug 04 2019 %H A083340 The CADO-NFS Development Team, <a href="https://gitlab.inria.fr/cado-nfs/cado-nfs">Cado-NFS</a>, An Implementation of the Number Field Sieve Algorithm, Release 2.3.0, 2017 %H A083340 Andrew Walker, <a href="http://web.archive.org/web/20080808141339/http://www.uow.edu.au/~ajw01/ecm/pluspp.txt">Factors of (n!)^2+1</a>. %H A083340 factordb.com, <a href="http://factordb.com/index.php?query=75%21%5E2%2B1">Status of 75!^2+1</a>. %e A083340 a(1)=6 because (6!)^2+1=518401=13*39877 is a semiprime. %t A083340 Select[Range[60],PrimeOmega[(#!)^2+1]==2&] (* _Harvey P. Dale_, Dec 12 2018 *) %Y A083340 Cf. A020549, A001358, A083341, A046029, A282706. %K A083340 nonn,more,hard %O A083340 1,1 %A A083340 _Hugo Pfoertner_, Apr 24 2003 %E A083340 a(15) from _Hugo Pfoertner_, Jul 13 2019 %E A083340 a(16), a(17) from _Hugo Pfoertner_, Aug 04 2019