

A007493


Decimal expansion of Wallis' number, the real root of x^3  2*x  5.
(Formerly M0036)


4



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, 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, 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
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OFFSET

1,1


COMMENTS

"The real solution to the equation x^3  2x  5 = 0. This equation was solved by [the English mathematician John] Wallis [16161703] to illustrate Newton's method for the numerical solution of equations.
"It has since served as a test for many subsequent methods of approximation and its real root is now known to 4000 digits." [Gruenberger]


REFERENCES

F. Gruenberger, Computer Recreations, Scientific American, 250 (No. 4, 1984), 1926.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. E. Smith, A Source Book in Mathematics, McGrawHill, 1929, pp. 247248.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 27.


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000
W. G. Horner, A new method of solving numerical equations of all orders, by continuous approximation, Phil. Trans. Royal Soc., 1819, pp. 308335.
D. Olivastro, Ancient Puzzles, Bantam Books, NY (1993), cover page and pp. 5859. (Annotated scanned copy)
Eric Weisstein's World of Mathematics, Wallis's Constant


EXAMPLE

2.094551481542326591482386540579302963857306105628239180304128529...


MATHEMATICA

RealDigits[ N[ 1/3* (135/2  (3*Sqrt[1929])/2)^(1/3) + (1/2*(45 + Sqrt[1929]) )^(1/3) / 3^(2/3), 100]][[1]]


PROG

(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=(rd)*10; write("b007493.txt", n, " ", d)); } \\ Harry J. Smith, May 03 2009
(PARI) polrootsreal(x^32*x5)[1] \\ Charles R Greathouse IV, Apr 14 2014


CROSSREFS

Cf. A058297 Continued fraction.
Sequence in context: A197330 A168229 A019693 * A262177 A136319 A176057
Adjacent sequences: A007490 A007491 A007492 * A007494 A007495 A007496


KEYWORD

cons,nonn


AUTHOR

N. J. A. Sloane, Robert G. Wilson v


EXTENSIONS

Final digits of sequence corrected using the bfile.  N. J. A. Sloane, Aug 30 2009


STATUS

approved



