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Search: id:A123626
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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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+0
2
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| 1, 5, 102, 2970, 16450, 997220, 18268740, 37403100, 2539082700, 23305436, 141249408300, 97836438700
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It turns out that A123625(n)/a(n) are good approximations to Pi/sqrt(3). In a similar vein R. Apery discovered in 1978 a 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
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Frits Beukers, A rational approach to Pi, NAW 5/1 nr.4, december 2000, p. 378
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FORMULA
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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
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Cf. A123625.
Adjacent sequences: A123623 A123624 A123625 this_sequence A123627 A123628 A123629
Sequence in context: A113073 A057207 A124986 this_sequence A052138 A007619 A057016
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KEYWORD
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frac,nonn
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AUTHOR
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Benoit Cloitre (abmt(AT)orange.fr), Oct 03 2006
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