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A002485
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Numerators of convergents to Pi.
(Formerly M3097 N1255)
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| 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.
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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..201
Marc Daumas, Des implantations differentes ..., see p. 8.
G. P. Michon, Continued Fractions
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
Index entries for sequences related to the number Pi
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EXAMPLE
| The convergents are 0, 1, 3, 22/7, 333/106, 355/113, 103993/33102, ... = A002485/A002486
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MAPLE
| Digits := 60: E := Pi; convert(evalf(E), confrac, 50, 'cvgts'): cvgts;
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MATHEMATICA
| Join[{0, 1}, Numerator @ Convergents[Pi, 29]] (* From Jean-François Alcover, Apr 8 2011 *)
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CROSSREFS
| Cf. A002486, A046947, A072398/A072399.
Sequence in context: A102223 A189897 A046947 * A193193 A099750 A196734
Adjacent sequences: A002482 A002483 A002484 * A002486 A002487 A002488
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KEYWORD
| nonn,easy,nice,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Extended and corrected by David Sloan, Sep 23, 2002.
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