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 A058233 #32 Sep 28 2021 01:26:00
%S A058233 2,17,1459,2999
%N A058233 Primes p such that p#+1 is divisible by the next prime after p.
%C A058233 No additional terms through the 100000th prime. - _Harvey P. Dale_, Mar 12 2014
%C A058233 a(5) > prime(1400000) = 22182343. - _Robert Price_, Apr 02 2018
%H A058233 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_117.htm">Puzzle 117: Certain p#+1 values</a>, The Prime Puzzles and Problems Connection.
%e A058233 2*3*5*7*11*13*17+1 is divisible by 19.
%t A058233 primorial[n_] := Product[ Prime[k], {k, 1, PrimePi[n]}]; Select[ Prime[ Range[1000]], Divisible[ primorial[#] + 1, NextPrime[#]] &] (* _Jean-François Alcover_, Aug 19 2013 *)
%t A058233 Module[{prs=Prime[Range[500]]},Transpose[Select[Thread[{Rest[ FoldList[ Times, 1,prs]], prs}], Divisible[ First[#]+1, NextPrime[Last[#]]]&]][[2]]] (* _Harvey P. Dale_, Mar 12 2014 *)
%o A058233 (Python)
%o A058233 from sympy import nextprime
%o A058233 A058233_list, p, q, r = [], 2, 3, 2
%o A058233 for _ in range(10**3):
%o A058233 if (r+1) % q == 0:
%o A058233 A058233_list.append(p)
%o A058233 r *= q
%o A058233 p, q = q, nextprime(q) # _Chai Wah Wu_, Sep 27 2021
%Y A058233 Cf. A006862, A066735, A341804.
%K A058233 nice,nonn,more
%O A058233 1,1
%A A058233 _Carlos Rivera_, Dec 01 2000