%I #18 Oct 27 2023 10:39:55

%S 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,

%T 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,

%U 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

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

%C Algebraic integer of degree 3. - _Charles R Greathouse IV_, Apr 18 2016

%H Tito Piezas III, <a href="https://sites.google.com/view/tpiezas/0022-part-1-the-163-dimensions">The 163 Dimensions of the Moonshine Functions</a>, A Collection of Algebraic Identities.

%H <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>

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

%F 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.

%F Equals 2 + A160332. - _R. J. Mathar_, Sep 29 2015

%e 5.318628217750185659109680153318022467721919808836900260228...

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

%o (PARI) solve(x=5, 6, x^3 - 6*x^2 + 4*x - 2) \\ _Michel Marcus_, Sep 27 2015

%o (PARI) polrootsreal(x^3-6*x^2+4*x-2)[1] \\ _Charles R Greathouse IV_, Apr 18 2016

%Y Cf. A060295.

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Sep 27 2015