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%I #11 Feb 23 2021 05:26:20
%S 2,9,185,5387,29837,1808757,33135829,67841719,4605386587,42271385,
%T 256198086973,177455670313
%N Numerators of the convergents of the continued fraction for Pi/sqrt(3) using the classical continued fraction for arctan(x).
%C 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 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 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 Cf. A093602, A123626.
%K frac,nonn,more
%O 1,1
%A _Benoit Cloitre_, Oct 03 2006
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