Search: id:A007493
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%I A007493 M0036
%S A007493 2,0,9,4,5,5,1,4,8,1,5,4,2,3,2,6,5,9,1,4,8,2,3,8,6,5,4,0,5,7,9,3,0,2,9,
%T A007493 6,3,8,5,7,3,0,6,1,0,5,6,2,8,2,3,9,1,8,0,3,0,4,1,2,8,5,2,9,0,4,5,3,1,2,
%U A007493 1,8,9,9,8,3,4,8,3,6,6,7,1,4,6,2,6,7,2,8,1,7,7,7,1,5,7,7,5,7,8,6,0,8,3
%N A007493 Decimal expansion of Wallis' number, the real root of x^3 - 2*x - 5.
%C A007493 "The real solution to the equation x^3 - 2x - 5 = 0. This equation was 
               solved by [the English mathematicaian John] Wallis [1616-1703] to 
               illustrate Newton's method for the numerical solution of equations.
%C A007493 "It has since served as a test for many subsequent methods of approximation 
               and its real root is now known to 4000 digits." [Gruenberger]
%D A007493 F. Gruenberger, Computer Recreations, Scientific American, 250 (No. 4, 
               1984), 19-26.
%D A007493 W. G. Horner, A new method of solving numerical equations of all orders, 
               by continuous approximation, Phil. Trans. Royal Soc., 1819, pp. 308-335.
%D A007493 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007493 D. E. Smith, A Source Book in Mathematics, McGraw-Hill, 1929, pp. 247-248.
%D A007493 David Wells, "The Penguin Dictionary of Curious and Interesting Numbers,
               " Revised Edition, Penguin Books, London, England, 1997, page 27.
%H A007493 Harry J. Smith, <a href="b007493.txt">Table of n, a(n) for n=1,...,20000</
               a>
%H A007493 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               WallissConstant.html">Wallis's Constant</a>
%e A007493 2.094551481542326591482386540579302963857306105628239180304128529...
%t A007493 RealDigits[ N[ 1/3* (135/2 - (3*Sqrt[1929])/2)^(1/3) + (1/2*(45 + Sqrt[1929]) 
               )^(1/3) / 3^(2/3), 100]][[1]]
%o A007493 (PARI) { default(realprecision, 20080); x=NULL; p=x^3 - 2*x - 5; rs=polroots(p); 
               r=real(rs[1]); for (n=1, 20000, d=floor(r); r=(r-d)*10; write("b007493.txt", 
               n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 03 2009]
%Y A007493 Cf. A058297 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 03 2009]
%Y A007493 Sequence in context: A071120 A156649 A019693 this_sequence A136319 A152566 
               A021481
%Y A007493 Adjacent sequences: A007490 A007491 A007492 this_sequence A007494 A007495 
               A007496
%K A007493 cons,nonn
%O A007493 1,1
%A A007493 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A007493 Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               May 19 2009
%E A007493 Final digits of sequence corrected using the b-file. - N. J. A. Sloane, 
               Aug 30 2009

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