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.
6! - (6-1)! + 1 = 601 is prime.
5 is a term since 5*5! - 1 = 599 is prime.
Select[Range[2600],PrimeQ[#(#!)-1]&] (* Because a(22) generates a 7524 digit number to be tested for primality, the program takes a long time to run. *) (* Harvey P. Dale, May 27 2014 *)
8 is in the sequence because 8*8!+ 11 is prime.
<< NumberTheory`NumberTheoryFunctions`;v={};Do[If[PrimeQ [n*n!+NextPrime[n]], v=Append[v, n];Print[v]], {n, 2400}]
isok(n) = isprime(n*n! + nextprime(n+1)); \\ Michel Marcus, Sep 13 2018
f[n_]:=n!-n; lst={};Do[If[PrimeQ[f[n+1]-f[n]],AppendTo[lst,f[n+1]-f[n]]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 27 2009 *)
Select[#[[2]]-#[[1]]-1&/@Partition[Range[100]!,2,1],PrimeQ] (* Harvey P. Dale, Feb 17 2015 *)
3 is in the sequence because 3*3! - 5 = 13 is prime. 8 is in the sequence because 8*8! - 11 = 322549 is prime.
<< NumberTheory`NumberTheoryFunctions`;v={};Do[If[PrimeQ [n*n!-NextPrime[n]], v=Append[v, n];Print[v]], {n, 2150}]
Select[Range[900],PrimeQ[# #!-NextPrime[#]]&] (* The program generates the first 21 terms of the sequence. To select more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Aug 16 2023 *)
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