A343948 Decimal expansion of -(1 + (5/9)^(1/3)*((9+4*sqrt(6))^(1/3) - (4*sqrt(6)-9)^(1/3)))/4 (negated).

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

Offset

0,1

Comments

Abscissa of the minimum of 1+x+x^2+x^3+x^4.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Aaron Hendrickson and Claude Leibovici, On the minimum of 1+x+..+x^(2n), arXiv:2105.00135 [math.HO], 2021.

Index entries for algebraic numbers, degree 3.

Formula

Minimal polynomial: 4*x^3 - 3*x^2 + 2*x - 1. - Amiram Eldar, Jun 08 2026

Equals 1/4 + sqrt(5/3) * sinh(arcsinh(3*sqrt(3/5))/3)/2. - Vaclav Kotesovec, Jun 08 2026

Example

-0.605829586188268020990938731157

Mathematica

First[RealDigits[(1 + (5/9)^(1/3)*((#+9)^(1/3) - (#-9)^(1/3)))/4 & [4*Sqrt[6]], 10, 100]] (* Paolo Xausa, Feb 27 2025 *)

Prog

(PARI) -(1 + sqrtn(5/9, 3)*(sqrtn(9+4*sqrt(6), 3) - sqrtn(4*sqrt(6)-9, 3)))/4
(PARI) polrootsreal(4*x^3 - 3*x^2 + 2*x - 1)[1] \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Sequence in context: A096410 A098468 A196625 * A195368 A198426 A335614

Adjacent sequences: A343945 A343946 A343947 * A343949 A343950 A343951

Keyword

cons,nonn

Author

Michel Marcus, May 05 2021

Status

approved