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
Examples
0.5897545123014583842788017470960713624514351732283620723880793412350480241...
Crossrefs
Cf. A356030.
Programs
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Mathematica
First[RealDigits[N[Root[-1+#1+2 #1^3 &, 1, 0], 76]]] (* Stefano Spezia, Aug 19 2022 *)
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PARI
solve(x=0, 1, 2*x^3 + x - 1) \\ Michel Marcus, Aug 19 2022
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