

A007493


Decimal expansion of Wallis's 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

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

D. Olivastro, Ancient Puzzles, Bantam Books, NY (1993), cover page and pp. 5859. (Annotated scanned copy)


FORMULA

Equals (5/2  sqrt(643/108))^(1/3) + (5/2 + sqrt(643/108))^(1/3).  Michal Paulovic, Mar 19 2023


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


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS

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


STATUS

approved



