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 A357471 #12 Nov 09 2022 05:10:53
%S A357471 5,6,9,8,4,0,2,9,0,9,9,8,0,5,3,2,6,5,9,1,1,3,9,9,9,5,8,1,1,9,5,6,8,6,
%T A357471 4,8,8,3,9,7,9,7,4,3,9,1,2,8,9,4,0,2,2,0,5,4,4,7,3,1,0,7,9,6,5,6,7,4,
%U A357471 7,1,9,6,1,1,7,4,6,6
%N A357471 Decimal expansion of the real root of x^3 - x^2 + 2*x - 1.
%C A357471 This equals r0 + 1/3 where r0 is the real root of y^3 + (5/3)*y - 11/27.
%C A357471 The other roots of x^3 - x^2 + 2*x - 1 are (1 + w1*((11 + 3*sqrt(69))/2)^(1/3) + ((11 - 3*sqrt(69))/2)^(1/3))/3 = 0.2150798545... + 1.3071412786...*i, and its complex conjugate, where w1 = (-1 + sqrt(3)*i)/2 = exp(2*Pi*i/3) is one of the complex conjugate roots of x^3 - 1.
%C A357471 Using hyperbolic functions these roots are (1 - sqrt(5)*(sinh((1/3)*arcsinh((11/50)*sqrt(5))) - sqrt(3)*cosh((1/3)*arcsinh((11/50)*sqrt(5)))*i))/3, and its complex conjugate.
%F A357471 r = (2 + (4*(11 + 3*sqrt(69)))^(1/3) - 20*(4*(11 + 3*sqrt(69)))^(-1/3))/6.
%F A357471 r = (2 + (4*(11 + 3*sqrt(69)))^(1/3) + w1*(4*(11 - 3*sqrt(69)))^(1/3))/6, where w1 = (-1 + sqrt(3)*i)/2 = exp(2*Pi*i/3) is one of the complex conjugate roots of x^3 - 1.
%F A357471 r = (1 + 2*sqrt(5)*sinh((1/3)*arcsinh((11/50)*sqrt(5))))/3.
%F A357471 r = (1/3) + (11/45)*Hyper2F1([1/3, 2/3],[3/2], -(11^2)/(2^2*5^3)). - _Gerry Martens_, Nov 04 2022
%e A357471 0.569840290998053265911399958119568648839797439128940220544731079656747...
%t A357471 RealDigits[x /. FindRoot[x^3 - x^2 + 2*x - 1, {x, 1}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, Oct 26 2022 *)
%Y A357471 Cf. A160389, A255524, A255249, A357470, A357472.
%K A357471 nonn,cons,easy
%O A357471 0,1
%A A357471 _Wolfdieter Lang_, Oct 25 2022