%I M2646 N1054
%S 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,
%T 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,
%U 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
%N Continued fraction expansion of Pi.
%C The first 5,821,569,425 terms were computed by _Eric W. Weisstein_ on Sep 18 2011.
%C The first 10,672,905,501 terms were computed by _Eric W. Weisstein_ on Jul 17 2013.
%C The first 15,000,000,000 terms were computed by _Eric W. Weisstein_ on Jul 27 2013.
%D P. Beckmann, "A History of Pi".
%D C. Brezinski, History of Continued Fractions and Pade' Approximants, SpringerVerlag, 1991; pp. 151152.
%D K. Y. Choong, D. E. Daykin and C. R. Rathbone, Regular continued fractions for pi and gamma, Math. Comp., 25 (1971), 403.
%D J. R. Goldman, The Queen of Mathematics, 1998, p. 50.
%D R. S. Lehman, A Study of Regular Continued Fractions. Report 1066, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, Feb 1959.
%D G. Lochs, Die ersten 968 Kettenbruchnenner von Pi. Monatsh. Math. 67 1963 311316.
%D C. D. Olds, Continued Fractions, Random House, NY, 1963; front cover of paperback edition.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H N. J. A. Sloane, <a href="/A001203/b001203.txt">Table of n, a(n) for n = 0..19999</a> [from the Plouffe web page]
%H James Barton, <a href="http://www.virtuescience.com/piinotherbases.html">Simple Continued Fraction Expansion of Pi</a> [From _Lekraj Beedassy_, Oct 27 2008]
%H E. Bombieri and A. J. van der Poorten, <a href="http://wwwcentre.mpce.mq.edu.au/alfpapers/a113.pdf">Continued fractions of algebraic numbers</a>
%H Exploratorium, <a href="http://chesswanks.com/seq/cfpi/">180 million terms of the simple CFE of pi</a>
%H Bill Gosper and Julian Ziegler Hunts, <a href="/A001203/a001203.gif">Animation</a>
%H B. Gourevitch, <a href="http://www.pi314.net">L'univers de Pi</a>
%H H. Havermann, <a href="http://chesswanks.com/pxp/cfpi.html">Simple Continued Fraction for Pi</a> [a 483 MB file containing 180 million terms]
%H Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/">20 megaterms of this sequence as computed by Hans Havermann</a>, starting in file CFPiTerms20aa.txt
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PiContinuedFraction.html">Pi Continued Fraction</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pi.html">Pi</a>
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%e Pi = 3.1415926535897932384...
%e = 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + ...))))
%e = [a_0; a_1, a_2, a_3, ...] = [3; 7, 15, 292, ...]
%p cfrac (Pi,70,'quotients');  _Zerinvary Lajos_, Feb 10 2007
%t ContinuedFraction[Pi, 98]
%o (PARI) contfrac(Pi) \\ contfracpnqn(%) is also useful!
%o (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]
%Y Cf. A000796 for decimal expansion. See A007541 or A033089, A033090 for records.
%Y Cf. A097545, A097546.
%K nonn,nice,cofr
%O 0,1
%A _N. J. A. Sloane_.
