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 A358184 #12 Sep 09 2023 16:22:14
%S A358184 7,3,8,9,8,3,6,2,1,5,0,4,5,0,6,2,3,7,3,2,3,4,6,2,5,4,0,6,7,1,0,8,7,5,
%T A358184 5,0,7,2,3,7,7,4,7,7,6,3,7,9,0,9,6,7,2,2,1,1,7,9,5,4,9,6,9,3,0,2,3,0,
%U A358184 2,0,3,1,5,9,8,0
%N A358184 Decimal expansion of the real root of 2*x^3 - x^2 + x - 1.
%C A358184 This equals r0 - 1/6 where r0 is the real root of y^3 - (7/12)*y - 11.
%C A358184 The other (complex) roots of 2*x^3 - x^2 + x - 1 are (1 + w1*(46 + 3*sqrt(249))^(1/3) + (46 - 3*sqrt(249))^(1/3))/6 = -0.1194918107... + 0.8138345589...*i, and its 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 A358184 Using hyperbolic functions these roots are (1 - sqrt(5)*(sinh((1/3)*arcsinh((46/25)*sqrt(5))) - sqrt(3)*cosh((1/3)*arcsinh((46/25)*sqrt(5)))*i))/6, and its complex conjugate.
%F A358184 r = (1 + (46 + 3*sqrt(249))^(1/3) - 5*(46+3*sqrt(249))^(-1/3))/6.
%F A358184 r = (1+ (46 + 3*sqrt(249))^(1/3) + w1*(46 - 3*sqrt(249))^(1/3))/6, where w1 = (-1 + sqrt(3)*i)/2 = exp(2*Pi*i/3).
%F A358184 r = (1 + 2*sqrt(5)*sinh((1/3)*arcsinh((46/25)*sqrt(5))))/6.
%F A358184 r = (1/6) + (46/45)*Hyper2F1([1/3, 2/3],[3/2], -(46^2/5^3)). - _Gerry Martens_, Nov 08 2022
%e A358184 0.73898362150450623732346254067108755072377477637909672211795496930230203...
%t A358184 RealDigits[x /. FindRoot[2*x^3 - x^2 + x - 1, {x, 1}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, Nov 08 2022 *)
%t A358184 RealDigits[Root[-1+x-x^2+2 x^3,1],10,120][[1]] (* _Harvey P. Dale_, Sep 09 2023 *)
%Y A358184 Cf. A358182, A358183.
%K A358184 nonn,cons,easy
%O A358184 0,1
%A A358184 _Wolfdieter Lang_, Nov 07 2022