

A001203


Simple continued fraction expansion of Pi.
(Formerly M2646 N1054)


53



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;
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OFFSET

0,1


COMMENTS

The first 30113021586 terms were computed by Syed Fahad on Apr 27 2021.


REFERENCES

P. Beckmann, "A History of Pi".
C. Brezinski, History of Continued Fractions and Padé Approximants, SpringerVerlag, 1991; pp. 151152.
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 311316.
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

Bill Gosper and Julian Ziegler Hunts, Animation
Ed Pegg, Jr., Sequence Pictures, Math Games column, Dec 08 2003 [Cached copy, with permission (pdf only)]
Eric Weisstein's World of Mathematics, 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, 1, 292, ...].


MAPLE



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
(Sage) continued_fraction(RealField(333)(pi)) # Peter Luschny, Feb 16 2015
(Python)
import itertools as it; import sympy as sp
list(it.islice(sp.continued_fraction_iterator(sp.pi), 100))


CROSSREFS



KEYWORD

nonn,nice,cofr


AUTHOR



EXTENSIONS

Word "Simple" added to the title by David Covert, Dec 06 2016


STATUS

approved



