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 A100614 #31 Feb 16 2025 08:32:55
%S A100614 3,4,5,8,9,10,11,30,76,163,271,273,354,721,1796,3733,4769,9316,12221,
%T A100614 41532
%N A100614 Numbers n such that (!n)/2 is prime, where !n = Sum_{k=0..n-1} k!.
%C A100614 No other terms below 50000. - _Serge Batalov_, Jul 23 2017
%D A100614 R. K. Guy, Unsolved Problems In Number Theory, B44.
%H A100614 Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/papers/lfact.html">Is the number of primes (of half the left handed factorials) finite?</a>.
%H A100614 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LeftFactorial.html">Left Factorial</a>
%H A100614 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%F A100614 When A014288(n-1) is prime.
%t A100614 s = 1; Do[s = s + n!; If[ PrimeQ[s/2], Print[n + 1]], {n, 10^3}] (* _Robert G. Wilson v_, Dec 02 2004 *)
%Y A100614 Cf. A014288, Left factorials: A003422.
%Y A100614 See A124375 for another version.
%K A100614 nonn,more
%O A100614 1,1
%A A100614 _R. K. Guy_, Dec 02 2004
%E A100614 a(14) from _Robert G. Wilson v_, Dec 02 2004
%E A100614 a(15)=1796 from _Ray Chandler_, Dec 02 2004
%E A100614 a(17) from _T. D. Noe_, Dec 04 2004
%E A100614 Corrected by adding a(16)=3733 from _Eric W. Weisstein_, Oct 29 2005
%E A100614 a(18)=9316 from _Eric W. Weisstein_, Dec 27 2005
%E A100614 a(19)=12221 from _Eric W. Weisstein_, Oct 19 2006
%E A100614 a(20)=41532 from _Serge Batalov_, Jul 22 2017