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 A123625 #14 May 05 2025 23:41:10 %S A123625 2,9,185,5387,29837,1808757,33135829,67841719,4605386587,42271385, %T A123625 256198086973,177455670313 %N A123625 Numerators of the convergents of the continued fraction for Pi/sqrt(3) using the classical continued fraction for arctan(x). %C A123625 It turns out that a(n)/A123626(n) are good approximations to Pi/sqrt(3). In a similar vein R. Apery discovered in 1978 an infinite sequence of good quality approximations to Pi^2. But for Pi itself, it was not until 1993 that Hata succeeded in doing so! %H A123625 Frits Beukers, <a href="http://www.nieuwarchief.nl/serie5/pdf/naw5-2000-01-4-372.pdf">A rational approach to Pi</a>, NAW 5/1 nr.4, december 2000, p. 378. %F A123625 Convergents are given by Pi/sqrt(3) = 2/(1+p_1/(3+p_2/(5+p_3/(7+p_4/(9+...))))) where p_i = i^2/3. %Y A123625 Cf. A093602, A123626. %K A123625 frac,nonn,more %O A123625 1,1 %A A123625 _Benoit Cloitre_, Oct 03 2006