This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357109 #10 Feb 11 2025 09:35:28
%S A357109 1,2,9,7,1,5,6,5,0,8,1,7,7,4,2,4,3,7,2,4,6,7,8,3,0,2,2,9,8,3,7,3,1,9,
%T A357109 5,5,5,5,3,8,0,5,5,8,1,3,7,0,3,9,6,8,2,2,8,3,6,1,5,9,4,4,3,0,8,8,4,3,
%U A357109 8,3,9,1,4,9,5,7,0
%N A357109 Decimal expansion of the real root of 2*x^3 - 2*x^2 - 1.
%C A357109 This equals r0 + 1/3 where r0 is the real root of y^3 - (1/3)*y - 31/54.
%C A357109 The other roots of 2*x^3 - 2*x^2 - 1 are (w1*((31 + 3*sqrt(105))/4)^(1/3) + w2*((31 - 3*sqrt(105))/4)^(1/3))/3 = -0.4819115874... + 0.6028125753...*i, and its complex conjugate, where w1 = (-1 + sqrt(3)*i)/2 and w2 = (-1 - sqrt(3)*i)/2 are the complex roots of x^3 - 1.
%C A357109 Using hyperbolic functions these roots are (-cosh((1/3)*arccosh(31/4)) + sqrt(3)*sinh((1/3)*arccosh(31/4))*i)/3, and its complex conjugate.
%H A357109 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>.
%F A357109 r = (((31 + 3*sqrt(105))/4)^(1/3) + ((31 + 3*sqrt(105))/4)^(-1/3) + 1)/3.
%F A357109 r = (((31 + 3*sqrt(105))/4)^(1/3) + ((31 - 3*sqrt(105))/4)^(1/3) + 1)/3.
%F A357109 r = (2*cosh((1/3)*arccosh(31/4))+1)/3.
%e A357109 1.29715650817742437246783022983731955553805581370396822836159443088438391495...
%t A357109 RealDigits[x /. FindRoot[2*x^3 - 2*x^2 - 1, {x, 1}, WorkingPrecision -> 100]][[1]] (* _Amiram Eldar_, Sep 29 2022 *)
%o A357109 (PARI) polrootsreal(2*x^3 - 2*x^2 - 1)[1] \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A357109 Cf. A273065.
%K A357109 nonn,cons,easy
%O A357109 1,2
%A A357109 _Wolfdieter Lang_, Sep 29 2022