Search: id:A002486
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%I A002486 M4456 N1886
%S A002486 1,0,1,7,106,113,33102,33215,66317,99532,265381,364913,1360120,1725033,
               25510582,
%T A002486 52746197,78256779,131002976,340262731,811528438,1963319607,4738167652,
               6701487259,
%U A002486 567663097408,1142027682075,1709690779483,2851718461558,44485467702853,
               136308121570117,1816491048114374,1952799169684491
%N A002486 Apart from two leading terms (which are present by convention), denominators 
               of convergents to pi (A002485 and A046947 give numerators).
%C A002486 Disregarding first two terms, integer diameters of circles beginning 
               with 1 and a(n+1) is the smallest integer diameter with corresponding 
               circumference nearer an integer than is the circumference of the 
               circle with diameter a(n). See PARI program. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), 
               Oct 06 2007
%C A002486 a(n+1) = numerator of fraction obtained from truncated continued fraction 
               expansion of 1/Pi to n terms. - Artur Jasinski (grafix(AT)csl.pl), 
               Mar 25 2008
%D A002486 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002486 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002486 P. Beckmann, A History of Pi. Golem Press, Boulder, CO, 2nd ed., 1971, 
               p. 171 (but beware errors).
%D A002486 E. B. Burger, Diophantine Olympics ..., Amer. Math. Monthly, 107 (Nov. 
               2000), 822-829.
%D A002486 CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 88.
%D A002486 P. Finsler, Ueber die Faktorenzerlegung natuerlicher Zahlen, Elemente 
               der Mathematik, 2 (1947), 1-11, see p. 7.
%D A002486 K. H. Rosen et al., eds., Handbook of Discrete and Combinatorial Mathematics, 
               CRC Press, 2000; p. 293.
%H A002486 T. D. Noe, <a href="b002486.txt">Table of n, a(n) for n=0..201</a>
%H A002486 <a href="Sindx_Ph.html#Pi314">Index entries for sequences related to 
               the number Pi</a>
%H A002486 Marc Daumas, <a href="http://www.ipsl.jussieu.fr/~omamce/SP/Oct00/Marc_Daumas.pdf">
               Des implantations differentes ...</a>, see p. 8.
%H A002486 G. P. Michon, <a href="http://home.att.net/~numericana/answer/fractions.htm">
               Final Answers</a>
%H A002486 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Pi.html">Link to a section of The World of Mathematics.</a>
%H A002486 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PiContinuedFraction.html">Link to a section of The World of Mathematics.</
               a>
%H A002486 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PiApproximations.html">Pi Approximations</a>
%e A002486 The convergents are 3, 22/7, 333/106, 355/113, 103993/33102, ...
%p A002486 Digits := 60: E := Pi; convert(evalf(E),confrac,50,'cvgts'): cvgts;
%p A002486 with(numtheory):cf := cfrac (Pi,100): seq(nthdenom (cf,i), i=-2..28 ); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 07 2007
%t A002486 b = {}; Do[c = Numerator[FromContinuedFraction[ContinuedFraction[1/Pi, 
               n]]]; AppendTo[b, c], {n, 1, 20}]; b - Artur Jasinski (grafix(AT)csl.pl), 
               Mar 25 2008
%o A002486 (PARI) /* Program calculates a(n) (slowly) without continued fraction 
               function */ {c=frac(Pi); print1("1, 0, 1, "); for(diam=2,500000000, 
               cm=diam*Pi;cmin=min(cm-floor(cm),ceil(cm)-cm);\ if(cmin<c,print1(diam,
               ", ");c=cmin))} /* or could use cmin=min(frac(cm),1-frac(cm)) above 
               */ - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 06 2007
%Y A002486 Cf. A002485, A072398/A072399.
%Y A002486 Sequence in context: A145666 A096131 A049210 this_sequence A145167 A141358 
               A141362
%Y A002486 Adjacent sequences: A002483 A002484 A002485 this_sequence A002487 A002488 
               A002489
%K A002486 nonn,easy,nice,frac
%O A002486 0,4
%A A002486 N. J. A. Sloane (njas(AT)research.att.com).
%E A002486 Extended and corrected by David Sloan, Sep 23, 2002.

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