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 A129978 #21 Sep 24 2024 14:14:27
%S A129978 2,3,4,5,6,7,12,16,19,21,22,25,41,114,181,236,2003,6138
%N A129978 Numbers k such that A120265(k) = numerator(Sum_{j=1..k} 1/j!) is a prime.
%C A129978 Corresponding primes are A120265(a(n)) = {3, 5, 41, 103, 1237, 433, 164611949, 35951249665217, 52255141388393, 43894318766250120011, 386270005143001056097, 53952693026046706215979, 1249584099900912571604389306768231303904375213027, ...}.
%C A129978 a(17) > 1000; A120265(1000) ~ 2.9*10^2564 = (e-1)*A061355(1000). - _M. F. Hasler_, Jun 18 2007
%t A129978 Do[ f=Numerator[ Sum[ 1/k!, {k,1,n} ] ]; If[ PrimeQ[f], Print[{n,f}] ], {n,1,236} ]
%t A129978 Flatten[Position[Numerator[Accumulate[1/Range[2150]!]],_?PrimeQ]] (* _Harvey P. Dale_, May 03 2013 *)
%o A129978 (PARI) my(t=0); for( n=1,1000, if( ispseudoprime( numerator( t+=1/n!)), print1( n", " ))) \\ _M. F. Hasler_, Jun 18 2007
%Y A129978 Cf. A120265, A061354, A061355.
%K A129978 more,nonn
%O A129978 1,1
%A A129978 _Alexander Adamchuk_, Jun 13 2007
%E A129978 Edited by _M. F. Hasler_, Jun 18 2007
%E A129978 a(17) from _Alexander Adamchuk_, May 02 2010
%E A129978 a(18) from _Michael S. Branicky_, Sep 24 2024