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 A059457 #18 Feb 20 2024 10:34:49
%S A059457 1,3,25,111,1583,5877,118943,1239213,6500369,6228669,200696339,
%T A059457 3293919963,125884243831,122175729021,5401896940303,121054306890369,
%U A059457 868338554787383,848589287072283,867261322002923,24637097377492167
%N A059457 Numerator of Sum_{k=0..n} (-1)^k/(3*k+1).
%C A059457 The denominators of Sum_{k = 0..n} (-1)^k/(3*k+1) agree with A051536 up to n = 44 but differ at n = 45. - _Peter Bala_, Feb 18 2024
%H A059457 G. C. Greubel, <a href="/A059457/b059457.txt">Table of n, a(n) for n = 0..1000</a>
%F A059457 Sum_{k>=0} (-1)^k/(3*k+1) = (log(2)*sqrt(3) + Pi)/(3*sqrt(3)).
%F A059457 a(n) = the numerator of the continued fraction 1/(1 + 1^2/(3 + 4^2/(3 + ... + (3*n-2)^2/(3)))). - _Peter Bala_, Feb 18 2024
%t A059457 Table[Numerator[Sum[(-1)^k/(3*k + 1), {k, 0, n}]], {n, 0, 50}] (* _G. C. Greubel_, Oct 04 2017 *)
%o A059457 (PARI) a(n)=numerator(sum(k=0,n,(-1)^k/(3*k+1)))
%K A059457 frac,nonn
%O A059457 0,2
%A A059457 _Benoit Cloitre_, Oct 19 2002
%E A059457 Corrected by _T. D. Noe_, Oct 25 2006