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A123626
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Denominators of the convergents of the continued fraction for Pi/sqrt(3) using the classical continued fraction for arctan(x).
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1
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1, 5, 102, 2970, 16450, 997220, 18268740, 37403100, 2539082700, 23305436, 141249408300, 97836438700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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!
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REFERENCES
| Frits Beukers, A rational approach to Pi, NAW 5/1 nr.4, december 2000, p. 378
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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
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CROSSREFS
| Cf. A123625.
Sequence in context: A113073 A057207 A124986 * A197799 A052138 A142418
Adjacent sequences: A123623 A123624 A123625 * A123627 A123628 A123629
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KEYWORD
| frac,nonn
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AUTHOR
| Benoit Cloitre (abmt(AT)orange.fr), Oct 03 2006
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