A262674 Decimal expansion of the real root of x^3 - 6x^2 + 4x - 2.

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

Offset: 1

Author

Jean-François Alcover, Sep 27 2015

Keywords

• nonn
• cons
• easy

Comments

Algebraic integer of degree 3. - Charles R Greathouse IV, Apr 18 2016

Examples

			5.318628217750185659109680153318022467721919808836900260228...
		

Links

• Tito Piezas III, The 163 Dimensions of the Moonshine Functions, A Collection of Algebraic Identities.
• Index entries for algebraic numbers, degree 3

Crossrefs

Cf. A060295.

Programs

Mathematica

RealDigits[Root[#^3 - 6#^2 + 4# - 2&, 1], 10, 106] // First

PARI

solve(x=5, 6, x^3 - 6*x^2 + 4*x - 2) \\ Michel Marcus, Sep 27 2015

PARI

polrootsreal(x^3-6*x^2+4*x-2)[1] \\ Charles R Greathouse IV, Apr 18 2016

Formula

Equals (1/3)*(6 + (135 - 3*sqrt(489))^(1/3) + (3*(45 + sqrt(489)))^(1/3)).

Also equals exp(Pi*i/24)*eta(tau)/eta(2*tau), where eta is Dedekind's eta function and tau = (1 + sqrt(163) i) / 2.

Equals 2 + A160332. - R. J. Mathar, Sep 29 2015