A335864 Decimal expansion of the negative of the zero x3 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.

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

Offset

0,1

Comments

For details and links see A335862.

Links

Table of n, a(n) for n=0..96.

Wolfdieter Lang, A list of representative simple difference sets of the Singer type for small orders m, Karlsruher Institut für Technologie (Karlsruhe, Germany 2020).

Formula

-x3 = (1/3)*(2 - (1/2)*(1 + sqrt(3)*i)*(179 + 3*sqrt(3)*sqrt(269)*i)^(1/3) - (1/2)*(1 - sqrt(3)*i)*(179 - 3*sqrt(3)*sqrt(269)*i)^(1/3)), where i is the imaginary unit.

Example

-x3 = 0.758886842296941304849382284375859546...

Maple

evalf((f-> (sqrt(34)*(cos(f)-sin(f)*sqrt(3))-2)/3)(arctan(sqrt(807)*3/179)/3), 120);  # Alois P. Heinz, Nov 17 2020

Mathematica

With[{j = Sqrt[3] I, k = 3 Sqrt[3] Sqrt[269] I}, First@ RealDigits[Re[(1/3) (2 - (1/2) (1 + j) (179 + k)^(1/3) - (1/2) (1 - j) (179 - k)^(1/3))], 10, 97]] (* Michael De Vlieger, Nov 17 2020 *)

Crossrefs

Cf. A335862 (x1), A335863 (-x2).

Sequence in context: A081815 A115372 A277682 * A199961 A195059 A347352

Adjacent sequences: A335861 A335862 A335863 * A335865 A335866 A335867

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, Jun 29 2020

Status

approved