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A123626
Denominators of the convergents of the continued fraction for Pi/sqrt(3) using the classical continued fraction for arctan(x).
1
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
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
Sequence in context: A124986 A231830 A260024 * A210900 A197799 A266903
KEYWORD
frac,nonn,more
AUTHOR
Benoit Cloitre, Oct 03 2006
STATUS
approved