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 A024530 #45 Oct 05 2023 14:26:10
%S A024530 0,1,1,11,47,727,7141,151427,2366603,64131559,1636722341,57208085801,
%T A024530 1916138684507,85982424199597,3392993977055461,172553478253276697,
%U A024530 8530444564835173531,535885387802465283059,30766248305796169627529
%N A024530 Numerator of -Sum_{k=1..n} (-1)^k / prime(k).
%C A024530 Limit of the fractional values is A078437. - _Charles R Greathouse IV_, Apr 22 2011
%H A024530 Seiichi Manyama, <a href="/A024530/b024530.txt">Table of n, a(n) for n = 0..350</a> (terms n = 1..100 from T. D. Noe)
%F A024530 a(n+1) = a(n)*prime(n+1) + (-1)^n*primorial(prime(n)) for n >= 2. - _Alexandre Herrera_, Sep 03 2023
%e A024530 0/1, 1/2, 1/6, 11/30, 47/210, 727/2310, 7141/30030, 151427/510510, ...
%p A024530 A024530 := n->numer(add((-1)^(k+1)/ithprime(k),k=1..n));
%t A024530 a[n_] := Numerator[ -Total[(-1)^Range[n] / Prime[ Range[n]]]]; Table[a[n], {n, 0, 18}] (* _Jean-François Alcover_, Dec 12 2011 *)
%o A024530 (PARI)
%o A024530 a(n)=numerator(-sum(k=1,n,(-1)^k/prime(k)));
%o A024530 concat(0, vector(33,n,a(n))) /* show terms */
%Y A024530 Denominators are A002110.
%Y A024530 Cf. A024451, A078437.
%K A024530 nonn,frac,easy,nice
%O A024530 0,4
%A A024530 _Clark Kimberling_
%E A024530 a(0)=0 prepended by _Seiichi Manyama_, Jul 25 2021