A123625 Numerators of the convergents of the continued fraction for Pi/sqrt(3) using the classical continued fraction for arctan(x).

2, 9, 185, 5387, 29837, 1808757, 33135829, 67841719, 4605386587, 42271385, 256198086973, 177455670313

Offset

1,1

Comments

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!

Links

Table of n, a(n) for n=1..12.

Frits Beukers, A rational approach to Pi, NAW 5/1 nr.4, december 2000, p. 378.

Formula

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.

Crossrefs

Cf. A093602, A123626.

Sequence in context: A349691 A078524 A041795 * A216692 A367901 A069649

Adjacent sequences: A123622 A123623 A123624 * A123626 A123627 A123628

Keyword

frac,nonn,more

Author

Benoit Cloitre, Oct 03 2006

Status

approved