A160332 Decimal expansion of the one real root of x^3 - 8x - 10.

3, 3, 1, 8, 6, 2, 8, 2, 1, 7, 7, 5, 0, 1, 8, 5, 6, 5, 9, 1, 0, 9, 6, 8, 0, 1, 5, 3, 3, 1, 8, 0, 2, 2, 4, 6, 7, 7, 2, 1, 9, 1, 9, 8, 0, 8, 8, 3, 6, 9, 0, 0, 2, 6, 0, 2, 2, 8, 0, 9, 1, 9, 9, 5, 8, 4, 0, 1, 9, 5, 8, 9, 7, 4, 5, 7, 3, 2, 1, 8, 7, 4, 3, 6, 6, 5, 3, 4, 5, 9, 1, 0, 7, 4, 8, 7, 1, 5, 4, 0, 0, 4, 5, 5, 8

Offset: 1

Author

Harry J. Smith, May 11 2009

Keywords

• nonn
• easy
• cons

Examples

			3.31862821775018565910968015331802246772191980883690026022809199584019...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Adam P. Goucher, Exotic continued fractions, 2013.
• Index entries for algebraic numbers, degree 3

Crossrefs

Cf. A002937 (continued fraction).

Programs

Mathematica

RealDigits[x /. FindRoot[x^3 - 8*x - 10, {x, 3}, WorkingPrecision -> 120]][[1]] (* Amiram Eldar, Jun 11 2023 *)

PARI

default(realprecision, 20080); x=NULL; p=x^3 - 8*x - 10; rs=polroots(p); r=real(rs[1]); for (n=1, 20000, d=floor(r); r=(r-d)*10; write("b160332.txt", n, " ", d));

PARI

sqrtn(5+sqrt(163/27), 3) + sqrtn(5-sqrt(163/27), 3); \\ Michel Marcus, Sep 06 2013

PARI

polrootsreal(x^3-8*x-10)[1] \\ Charles R Greathouse IV, Apr 14 2014

Formula

Equals (5+sqrt(163/27))^(1/3) + (5-sqrt(163/27))^(1/3).