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Search: id:A002485
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| A002485 |
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Numerators of convergents to Pi.
(Formerly M3097 N1255)
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+0
17
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| 0, 1, 3, 22, 333, 355, 103993, 104348, 208341, 312689, 833719, 1146408, 4272943, 5419351, 80143857, 165707065, 245850922, 411557987, 1068966896, 2549491779, 6167950454, 14885392687, 21053343141, 1783366216531, 3587785776203, 5371151992734, 8958937768937, 139755218526789, 428224593349304, 5706674932067741, 6134899525417045
(list; graph; listen)
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OFFSET
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0,3
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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. Golem Press, Boulder, CO, 2nd ed., 1971, p. 171 (but beware errors).
E. B. Burger, Diophantine Olympics ..., Amer. Math. Monthly, 107 (Nov. 2000), 822-829.
CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 88.
P. Finsler, Ueber die Faktorenzerlegung natuerlicher Zahlen, Elemente der Mathematik, 2 (1947), 1-11, see p. 7.
K. H. Rosen et al., eds., Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000; p. 293.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..201
Index entries for sequences related to the number Pi
Marc Daumas, Des implantations differentes ..., see p. 8.
G. P. Michon, Final Answers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Pi Approximations
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EXAMPLE
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The convergents are 0, 1, 3, 22/7, 333/106, 355/113, 103993/33102, ... = A002485/A002486
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MAPLE
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Digits := 60: E := Pi; convert(evalf(E), confrac, 50, 'cvgts'): cvgts;
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CROSSREFS
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Cf. A002486, A046947, A072398/A072399.
Sequence in context: A161967 A102223 A046947 this_sequence A099750 A156512 A119770
Adjacent sequences: A002482 A002483 A002484 this_sequence A002486 A002487 A002488
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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Extended and corrected by David Sloan, Sep 23, 2002.
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