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Search: id:A123625
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| A123625 |
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Numerators of the convergents of the continued fraction for Pi/sqrt(3) using the classical continued fraction for arctan(x). |
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3
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| 2, 9, 185, 5387, 29837, 1808757, 33135829, 67841719, 4605386587, 42271385, 256198086973, 177455670313
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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It turns out that a(n)/A123626(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. A123626.
Sequence in context: A053294 A078524 A041795 this_sequence A069649 A111832 A114563
Adjacent sequences: A123622 A123623 A123624 this_sequence A123626 A123627 A123628
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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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