# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a001203 Showing 1-1 of 1 %I A001203 M2646 N1054 #158 Mar 10 2023 11:15:25 %S A001203 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 A001203 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 A001203 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 A001203 Simple continued fraction expansion of Pi. %C A001203 The first 5821569425 terms were computed by _Eric W. Weisstein_ on Sep 18 2011. %C A001203 The first 10672905501 terms were computed by _Eric W. Weisstein_ on Jul 17 2013. %C A001203 The first 15000000000 terms were computed by _Eric W. Weisstein_ on Jul 27 2013. %C A001203 The first 30113021586 terms were computed by _Syed Fahad_ on Apr 27 2021. %D A001203 P. Beckmann, "A History of Pi". %D A001203 C. Brezinski, History of Continued Fractions and Padé Approximants, Springer-Verlag, 1991; pp. 151-152. %D A001203 J. R. Goldman, The Queen of Mathematics, 1998, p. 50. %D A001203 R. S. Lehman, A Study of Regular Continued Fractions. Report 1066, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, Feb 1959. %D A001203 G. Lochs, Die ersten 968 Kettenbruchnenner von Pi. Monatsh. Math. 67 1963 311-316. %D A001203 C. D. Olds, Continued Fractions, Random House, NY, 1963; front cover of paperback edition. %D A001203 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A001203 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A001203 N. J. A. Sloane, Table of n, a(n) for n = 0..19999 [from the Plouffe web page] %H A001203 James Barton, Simple Continued Fraction Expansion of Pi [From _Lekraj Beedassy_, Oct 27 2008] %H A001203 E. Bombieri and A. J. van der Poorten, Continued fractions of algebraic numbers %H A001203 K. Y. Choong, D. E. Daykin and C. R. Rathbone, Regular continued fractions for pi and gamma, Math. Comp., 25 (1971), 403. %H A001203 Sebastian M. Cioabă and Werner Linde, A Bridge to Advanced Mathematics: from Natural to Complex Numbers, Amer. Math. Soc. (2023) Vol. 58, see page 360. %H A001203 Francesco Dolce and Pierre-Adrien Tahay, Column representation of Sturmian words in cellular automata, Czech Technical University (Prague, Czechia, 2022). %H A001203 Eduardo Dorrego López and Elías Fuentes Guillén, An Annotated Translation of Lambert's Vorläufige Kenntnisse (1766/1770), In: Irrationality, Transcendence and the Circle-Squaring Problem. Logic, Epistemology, and the Unity of Science (LEUS 2023) Springer, Cham. Vol 58. %H A001203 Exploratorium, 180 million terms of the simple CFE of pi %H A001203 Syed Fahad, 30 billion terms of the simple continued fraction of Pi %H A001203 Bill Gosper, answer to: Did Gosper or the Borweins first prove Ramanujans formula?, History of Science and Mathematics Stack Exchange, April 2020. %H A001203 Bill Gosper and Julian Ziegler Hunts, Animation %H A001203 B. Gourevitch, L'univers de Pi %H A001203 Hans Havermann, Simple Continued Fraction for Pi [a 483 MB file containing 180 million terms] %H A001203 Hans Havermann, Binary plot of 2^10 terms %H A001203 Maxim Sølund Kirsebom, Extreme Value Theory for Hurwitz Complex Continued Fractions, Entropy (2021) Vol. 23, No. 7, 840. %H A001203 Antony Lee, Diophantine Approximation and Dynamical Systems, Master's Thesis, Lund University (Sweden 2020). %H A001203 Sophie Morier-Genoud and Valentin Ovsienko, On q-deformed real numbers, arXiv:1908.04365 [math.QA], 2019. %H A001203 Ed Pegg, Jr., Sequence Pictures, Math Games column, Dec 08 2003. %H A001203 Ed Pegg, Jr., Sequence Pictures, Math Games column, Dec 08 2003 [Cached copy, with permission (pdf only)] %H A001203 Simon Plouffe, 20 megaterms of this sequence as computed by Hans Havermann, starting in file CFPiTerms20aa.txt %H A001203 Denis Roegel, Lambert's proof of the irrationality of Pi: Context and translation, hal-02984214 [math.HO], 2020. %H A001203 N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 5. %H A001203 Eric Weisstein's World of Mathematics, Pi Continued Fraction %H A001203 Eric Weisstein's World of Mathematics, Pi %H A001203 G. Xiao, Contfrac %H A001203 Index entries for continued fractions for constants %H A001203 Index entries for sequences related to the number Pi %e A001203 Pi = 3.1415926535897932384... %e A001203 = 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + ...)))) %e A001203 = [a_0; a_1, a_2, a_3, ...] = [3; 7, 15, 1, 292, ...]. %p A001203 cfrac (Pi,70,'quotients'); # _Zerinvary Lajos_, Feb 10 2007 %t A001203 ContinuedFraction[Pi, 98] %o A001203 (PARI) contfrac(Pi) \\ contfracpnqn(%) is also useful! %o A001203 (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 %o A001203 (Sage) continued_fraction(RealField(333)(pi)) # _Peter Luschny_, Feb 16 2015 %o A001203 (Python) %o A001203 import itertools as it; import sympy as sp %o A001203 list(it.islice(sp.continued_fraction_iterator(sp.pi),100)) %o A001203 # _Nicholas Stefan Georgescu_, Feb 27 2023 %Y A001203 Cf. A000796 for decimal expansion. See A007541 or A033089, A033090 for records. %Y A001203 Cf. A097545, A097546. %K A001203 nonn,nice,cofr %O A001203 0,1 %A A001203 _N. J. A. Sloane_ %E A001203 Word "Simple" added to the title by _David Covert_, Dec 06 2016 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE