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 A109621 #15 Sep 14 2022 08:26:04
%S A109621 1,2,5,9,24,32,321,343,352,511,685,807,966,1079,1274,1381,2016,3226,
%T A109621 8130
%N A109621 Numbers n such that the numerator of Sum_{k=0..n} 1/k!, in reduced form, is prime.
%C A109621 Terms through 807 correspond to certified primes.
%C A109621 If it exists, a(20) > 14304. - _J.W.L. (Jan) Eerland_, Sep 13 2022
%e A109621 Sum_{k=0..9} 1/k! = 98641/36288 and 98641 is prime, so 9 is in the sequence.
%t A109621 s = 0; Do[s += 1/n!; k = Numerator[s]; If[PrimeQ[k], Print[n]], {n, 0, 3300}]
%t A109621 Flatten[Position[Accumulate[1/Range[0,3230]!],_?(PrimeQ[ Numerator[ #]]&)]] -1 (* _Harvey P. Dale_, Sep 25 2019 *)
%t A109621 n=0;Monitor[Parallelize[While[True,If[PrimeQ[Numerator[Sum[1/Factorial[k],{k,0,n}]]],Print[n]];n++];n],n] (* _J.W.L. (Jan) Eerland_, Sep 13 2022 *)
%Y A109621 Cf. A061354.
%K A109621 nonn,hard,more
%O A109621 1,2
%A A109621 _Ryan Propper_, Aug 01 2005
%E A109621 a(19) from _J.W.L. (Jan) Eerland_, Sep 13 2022