OFFSET
1,1
COMMENTS
Algebraic integer of degree 3. - Charles R Greathouse IV, Apr 18 2016
LINKS
Tito Piezas III, The 163 Dimensions of the Moonshine Functions, A Collection of Algebraic Identities.
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
EXAMPLE
5.318628217750185659109680153318022467721919808836900260228...
MATHEMATICA
RealDigits[Root[#^3 - 6#^2 + 4# - 2&, 1], 10, 106] // First
PROG
(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
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Sep 27 2015
STATUS
approved