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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 (list; constant; graph; refs; listen; history; text; internal format)
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 [1616-1703] 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), 19-26.

W. G. Horner, A new method of solving numerical equations of all orders, by continuous approximation, Phil. Trans. Royal Soc., 1819, pp. 308-335.

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, McGraw-Hill, 1929, pp. 247-248.

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

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=(r-d)*10; write("b007493.txt", n, " ", d)); } \\ Harry J. Smith, May 03 2009

(PARI) polrootsreal(x^3-2*x-5)[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

Fixed my PARI program, had -n Harry J. Smith, May 19 2009

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

STATUS

approved

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Last modified August 21 00:45 EDT 2017. Contains 290855 sequences.