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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
13
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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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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
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.
Adjacent sequences: A002482 A002483 A002484 this_sequence A002486 A002487 A002488
Sequence in context: A124567 A102223 A046947 this_sequence A099750 A119770 A132558
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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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njas
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EXTENSIONS
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Extended and corrected by David Sloan, Sep 23, 2002.
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