A335863 Decimal expansion of the negative of the zero x2 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.

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

Offset

1,2

Comments

For details and links see A335862.

Links

Table of n, a(n) for n=1..99.

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

-x2 = (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

-x2 = 1.7525178219298168184898392124373100279...

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, 99]] (* Michael De Vlieger, Nov 17 2020 *)

Crossrefs

Cf. A335862 (x1), A335864 (-x3).

Sequence in context: A258370 A135537 A212038 * A112545 A021934 A021097

Adjacent sequences: A335860 A335861 A335862 * A335864 A335865 A335866

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, Jun 29 2020

Status

approved