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

Author

Benoit Cloitre, Oct 03 2006

Keywords

• frac
• nonn
• more

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

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

Crossrefs

Cf. A093602, A123625.

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.