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A160332 Decimal expansion of the one real root of x^3 - 8x - 10.

%I A160332 #24 Oct 27 2023 10:26:50
%S A160332 3,3,1,8,6,2,8,2,1,7,7,5,0,1,8,5,6,5,9,1,0,9,6,8,0,1,5,3,3,1,8,0,2,2,
%T A160332 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 A160332 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
%N A160332 Decimal expansion of the one real root of x^3 - 8x - 10.
%H A160332 Harry J. Smith, <a href="/A160332/b160332.txt">Table of n, a(n) for n = 1..20000</a>
%H A160332 Adam P. Goucher, <a href="http://cp4space.wordpress.com/2013/09/04/exotic-continued-fractions/">Exotic continued fractions</a>, 2013.
%H A160332 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>
%F A160332 Equals (5+sqrt(163/27))^(1/3) + (5-sqrt(163/27))^(1/3).
%e A160332 3.31862821775018565910968015331802246772191980883690026022809199584019...
%t A160332 RealDigits[x /. FindRoot[x^3 - 8*x - 10, {x, 3}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, Jun 11 2023 *)
%o A160332 (PARI) default(realprecision, 20080); x=NULL; p=x^3 - 8*x - 10; rs=polroots(p); r=real(rs[1]); for (n=1, 20000, d=floor(r); r=(r-d)*10; write("b160332.txt", n, " ", d));
%o A160332 (PARI) sqrtn(5+sqrt(163/27), 3) + sqrtn(5-sqrt(163/27), 3); \\ _Michel Marcus_, Sep 06 2013
%o A160332 (PARI) polrootsreal(x^3-8*x-10)[1] \\ _Charles R Greathouse IV_, Apr 14 2014
%Y A160332 Cf. A002937 (continued fraction).
%K A160332 nonn,easy,cons
%O A160332 1,1
%A A160332 _Harry J. Smith_, May 11 2009