A123626 Denominators of the convergents of the continued fraction for Pi/sqrt(3) using the classical continued fraction for arctan(x).

1, 5, 102, 2970, 16450, 997220, 18268740, 37403100, 2539082700, 23305436, 141249408300, 97836438700

Offset

1,2

Comments

It turns out that A123625(n)/a(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, A123625.

Sequence in context: A124986 A231830 A260024 * A210900 A197799 A266903

Adjacent sequences: A123623 A123624 A123625 * A123627 A123628 A123629

Keyword

frac,nonn,more

Author

Benoit Cloitre, Oct 03 2006

Status

approved