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Search: id:A001203
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| A001203 |
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Continued fraction for Pi.
(Formerly M2646 N1054)
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+0
26
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| 3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, 6, 6, 99, 1, 2, 2, 6, 3, 5, 1, 1, 6, 8, 1, 7, 1, 2, 3, 7, 1, 2, 1, 1, 12, 1, 1, 1, 3, 1, 1, 8, 1, 1, 2, 1, 6, 1, 1, 5, 2, 2, 3, 1, 2, 4, 4, 16, 1, 161, 45, 1, 22, 1, 2, 2, 1, 4, 1, 2, 24, 1, 2, 1, 3, 1, 2, 1
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
P. Beckmann, "A History of Pi".
C. Brezinski, History of Continued Fractions ans Pade' Approximants, Springer-Verlag, 1991; pp. 151-152.
K. Y. Choong, D. E. Daykin and C. R. Rathbone, Regular continued fractions for pi and gamma, Math. Comp., 25 (1971), 403.
J. R. Goldman, The Queen of Mathematics, 1998, p. 50.
R. S. Lehman, A Study of Regular Continued Fractions. Report 1066, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, Feb 1959.
G. Lochs, Die ersten 968 Kettenbruchnenner von Pi. Monatsh. Math. 67 1963 311-316.
C. D. Olds, Continued Fractions, Random House, NY, 1963; front cover of paperback edition.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [from the Plouffe web page]
Index entries for sequences related to the number Pi
E. Bombieri and A. J. van der Poorten, Continued fractions of algebraic numbers
Exploratorium, 180 million terms of the simple CFE of pi
B. Gourevitch, L'univers de Pi
H. Havermann, Simple Continued Fraction for Pi
S. Plouffe, 20 megaterms of this sequence as computed by Hans Havermann
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).
G. Xiao, Contfrac
Index entries for continued fractions for constants
James Barton, Simple Continued Fraction Expansion of Pi [From Lekraj Beedassy (blekraj(AT)yahoo.com), Oct 27 2008]
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EXAMPLE
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Pi = 3.1415926535897932384... = 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 07 2009]
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MAPLE
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cfrac (Pi, 70, 'quotients'); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 10 2007
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MATHEMATICA
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ContinuedFraction[Pi, 98]
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PROGRAM
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(PARI) contfrac(Pi) (contfracpnqn(%) is also useful!)
(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi); for (n=1, 20000, write("b001203.txt", n, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 14 2009]
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CROSSREFS
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Cf. A000796 for decimal expansion. See A033089 for records.
Cf. A097545, A097546.
Sequence in context: A146155 A106363 A128658 this_sequence A154883 A109732 A114396
Adjacent sequences: A001200 A001201 A001202 this_sequence A001204 A001205 A001206
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KEYWORD
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nonn,nice,cofr
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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