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A001203 Continued fraction expansion of Pi.
(Formerly M2646 N1054)
41
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; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The first 5,821,569,425 terms were computed by Eric W. Weisstein on Sep 18 2011.

The first 10,672,905,501 terms were computed by Eric W. Weisstein on Jul 17 2013.

The first 15,000,000,000 terms were computed by Eric W. Weisstein on Jul 27 2013.

REFERENCES

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.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..19999 [from the Plouffe web page]

James Barton, Simple Continued Fraction Expansion of Pi [From Lekraj Beedassy, Oct 27 2008]

E. Bombieri and A. J. van der Poorten, Continued fractions of algebraic numbers

Exploratorium, 180 million terms of the simple CFE of pi

Bill Gosper and Julian Ziegler Hunts, Animation

B. Gourevitch, L'univers de Pi

H. Havermann, Simple Continued Fraction for Pi [a 483 MB file containing 180 million terms]

Simon Plouffe, 20 megaterms of this sequence as computed by Hans Havermann, starting in file CFPiTerms20aa.txt

Eric Weisstein's World of Mathematics, Pi Continued Fraction

Eric Weisstein's World of Mathematics, Pi

G. Xiao, Contfrac

Index entries for continued fractions for constants

Index entries for sequences related to the number Pi

EXAMPLE

Pi = 3.1415926535897932384...

   = 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + ...))))

   = [a_0; a_1, a_2, a_3, ...] = [3; 7, 15, 292, ...]

MAPLE

cfrac (Pi, 70, 'quotients'); - Zerinvary Lajos, Feb 10 2007

MATHEMATICA

ContinuedFraction[Pi, 98]

PROG

(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])); } [Harry J. Smith, Apr 14 2009]

CROSSREFS

Cf. A000796 for decimal expansion. See A007541 or A033089, A033090 for records.

Cf. A097545, A097546.

Sequence in context: A106363 A128658 A234042 * A154883 A109732 A114396

Adjacent sequences:  A001200 A001201 A001202 * A001204 A001205 A001206

KEYWORD

nonn,nice,cofr

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 17 09:38 EDT 2014. Contains 246836 sequences.