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

%I A262674 #18 Oct 27 2023 10:39:55
%S A262674 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 A262674 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 A262674 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 A262674 Decimal expansion of the real root of x^3 - 6x^2 + 4x - 2.
%C A262674 Algebraic integer of degree 3. - _Charles R Greathouse IV_, Apr 18 2016
%H A262674 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 A262674 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>
%F A262674 Equals (1/3)*(6 + (135 - 3*sqrt(489))^(1/3) + (3*(45 + sqrt(489)))^(1/3)).
%F A262674 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 A262674 Equals 2 + A160332. - _R. J. Mathar_, Sep 29 2015
%e A262674 5.318628217750185659109680153318022467721919808836900260228...
%t A262674 RealDigits[Root[#^3 - 6#^2 + 4# - 2&, 1], 10, 106] // First
%o A262674 (PARI) solve(x=5, 6, x^3 - 6*x^2 + 4*x - 2) \\ _Michel Marcus_, Sep 27 2015
%o A262674 (PARI) polrootsreal(x^3-6*x^2+4*x-2)[1] \\ _Charles R Greathouse IV_, Apr 18 2016
%Y A262674 Cf. A060295.
%K A262674 nonn,cons,easy
%O A262674 1,1
%A A262674 _Jean-François Alcover_, Sep 27 2015