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 A129976 #15 Apr 28 2025 07:13:47
%S A129976 1,2,3,4,5,6,8,10,14,21,33,36,56,68,94,378,1943,2389,2710,5455,6804
%N A129976 Numbers k such that the numerator of Sum_{j=0..k} k^j/j! is a prime number.
%C A129976 The corresponding primes are A120266(a(n)) = {2, 5, 13, 103, 1097, 1223, ...}
%C A129976 a(22) > 10^4. - _Michael S. Branicky_, Apr 27 2025
%e A129976 Sum_{j=0..4} 4^j/j! = 103/3. The numerator is a prime, hence 4 is in the sequence.
%t A129976 Do[ f=Numerator[Sum[n^k/k!,{k,0,n}]]; If[PrimeQ[f], Print[{n,f}]], {n, 1, 378}]
%Y A129976 Cf. A120266, A119029, A120267.
%K A129976 nonn,hard,more
%O A129976 1,2
%A A129976 _Alexander Adamchuk_, Jun 13 2007
%E A129976 Edited by _Stefan Steinerberger_, Jul 22 2007
%E A129976 a(17)-a(18) and a(20) from _Ryan Propper_, Jan 22 2008
%E A129976 a(19) and a(21) from _Michael S. Branicky_, Apr 26 2025