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 A053982 #33 Aug 12 2024 13:08:12
%S A053982 1,3,7,11,16,22,39,76,116,139,149,169,179,220,372,429,1216,2146,3176,
%T A053982 5382,5969,12271,15271,43903
%N A053982 Numbers k such that 1 + product of first k composite numbers is prime.
%t A053982 Composite[n_Integer] := (k = n + PrimePi[n] + 1; While[k - PrimePi[k] - 1 != n, k++ ]; k); Do[ If[ PrimeQ[ Product[ Composite[k], {k, 1, n} ] + 1], Print[ n ] ], {n, 1, 430} ]
%t A053982 Position[FoldList[Times,Select[Range[1500],CompositeQ]],_?(PrimeQ[#+1]&)]//Flatten (* _Harvey P. Dale_, Dec 20 2022 *)
%o A053982 (PARI) lista(kmax) = {my(m = 1, k = 0); forcomposite(c = 1, , k++; if(k > kmax, break); m *= c; if(isprime(m+1), print1(k, ", ")));} \\ _Amiram Eldar_, Jun 03 2024
%Y A053982 Cf. A002808, A000040, A049420, A049650, A057017, A140294.
%K A053982 nonn,more
%O A053982 1,2
%A A053982 _G. L. Honaker, Jr._, Apr 02 2000
%E A053982 More terms from _Jeppe Stig Nielsen_, Apr 16 2000 (terms from 76 on correspond to probable primes)
%E A053982 a(16)-a(17) from _Robert G. Wilson v_, Apr 20 2001
%E A053982 Edited by _T. D. Noe_, Oct 30 2008
%E A053982 a(18)-a(19) from _Amiram Eldar_, Jun 03 2024
%E A053982 a(20)-a(21) from _Michael S. Branicky_, Jun 04 2024
%E A053982 More terms via A049420 from _Jeppe Stig Nielsen_, Aug 12 2024