A089826 Decimal expansion of real root of 2*x^3+x^2-1.

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

Offset

0,1

Comments

This is also the decimal expansion of the real root of y^3 - y/12 - 53/108, that is, 0.8239647728..., after subtraction of 1/6. - Wolfdieter Lang, Aug 18 2022

Links

Table of n, a(n) for n=0..98.

G. Chen et al., Second neighborhood via first neighborhood in digraphs, Annals Combin., 7 (2000), 15-20.

Index entries for algebraic numbers, degree 3

Formula

From Wolfdieter Lang, Aug 18 2022: (Start)

Equals ((53 + 6*sqrt(78))^(1/3) + 1/(53 + 6*sqrt(78))^(1/3) - 1)/6.

Equals ((53 + 6*sqrt(78))^(1/3) + (53 - 6*sqrt(78))^(1/3) - 1)/6. (End)

Example

0.65729810613837599082505552...

Mathematica

RealDigits[x/.Solve[2x^3+x^2-1==0, x][[1]], 10, 120][[1]] (* Harvey P. Dale, Jun 03 2017 *)
RealDigits[Root[2*x^3+x^2-1, 1], 10, 120][[1]] (* Harvey P. Dale, Mar 04 2023 *)

Prog

(PARI) real(polroots(2*x^3+x^2-1)[1]) \\ Charles R Greathouse IV, Mar 25 2014
(PARI) polrootsreal(2*x^3+x^2-1)[1] \\ Charles R Greathouse IV, Oct 27 2023

Crossrefs

Sequence in context: A243091 A195786 A201330 * A211172 A152149 A338287

Adjacent sequences: A089823 A089824 A089825 * A089827 A089828 A089829

Keyword

nonn,cons

Author

N. J. A. Sloane, Jan 18 2004

Status

approved