login
A089826
Decimal expansion of real root of 2*x^3+x^2-1.
0
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
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
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Jan 18 2004
STATUS
approved