A356031 Decimal expansion of the real root of 2*x^3 + x - 1.

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

Offset

0,1

Links

Table of n, a(n) for n=0..75.

Formula

Equals (1/6)*(54+6*sqrt(87))^(1/3) - 1/(54+6*sqrt(87))^(1/3).

Equals ((54 + 6*sqrt(87))^(1/3) - (54 - 6*sqrt(87))^(1/3)*(1-sqrt(3)*i)/2)/6, with i the imaginary unit sqrt(-1).

Equals -sqrt(2/3) * sinh(log((sqrt(58) - 3*sqrt(6))/2)/3). - Vaclav Kotesovec, Aug 19 2022

Example

0.5897545123014583842788017470960713624514351732283620723880793412350480241...

Mathematica

First[RealDigits[N[Root[-1+#1+2 #1^3 &, 1, 0], 76]]] (* Stefano Spezia, Aug 19 2022 *)

Prog

(PARI) solve(x=0, 1, 2*x^3 + x - 1) \\ Michel Marcus, Aug 19 2022

Crossrefs

Cf. A356030.

Sequence in context: A197815 A257870 A338275 * A336003 A314578 A314577

Adjacent sequences: A356028 A356029 A356030 * A356032 A356033 A356034

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, Aug 19 2022

Status

approved