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 A124082 #21 Oct 03 2024 06:26:05
%S A124082 3,4,7,21,60
%N A124082 Numbers k such that prime(k)!/prime(k)# - 1 is prime.
%C A124082 No more terms through 1000. - _Ryan Propper_, Jan 27 2007
%C A124082 No more terms through 2500. - _Michael S. Branicky_, Oct 02 2024
%e A124082 1*2*3*4*5/(2*3*5) - 1 = 3, a prime, so a(1)=3 as 5=prime(3);
%e A124082 1*2*3*4*5*6*7/(2*3*5*7) - 1 = 23, a prime, so a(2)=4 as 7=prime(4);
%e A124082 1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17/(2*3*5*7*11*13*17) - 1 = 696729599, a prime, so a(3)=7 as 17=prime(7).
%t A124082 Primorial[n_] := Times @@ Select[Range[n], PrimeQ]; Do[k = Prime[n]; If[PrimeQ[k!/Primorial[k] - 1], Print[n]], {n, 10^3}] (* _Ryan Propper_, Jan 27 2007 *)
%t A124082 With[{nn=70},Position[#[[1]]/#[[2]]-1&/@Thread[{Prime[Range[ nn]]!,FoldList[ Times,Prime[Range[nn]]]}],_?PrimeQ]//Flatten] (* _Harvey P. Dale_, Jul 01 2020 *)
%o A124082 (PARI) isok(k) = isprime(prime(k)!/prod(i=1, k, prime(i)) - 1); \\ _Michel Marcus_, Sep 15 2019
%Y A124082 Cf. A092435 (p!/p#), A124083.
%K A124082 more,nonn
%O A124082 1,1
%A A124082 _Pierre CAMI_, Nov 25 2006