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 A358182 #14 Nov 09 2022 19:20:05
%S A358182 1,2,3,3,7,5,1,9,2,8,5,2,8,2,5,8,7,8,8,1,9,0,9,4,3,3,7,7,6,7,9,3,9,3,
%T A358182 0,3,5,1,9,1,1,2,7,2,3,7,5,3,1,1,8,6,4,9,4,2,3,2,0,0,9,8,8,7,0,2,7,5,
%U A358182 3,7,5,9,6,7,9,5
%N A358182 Decimal expansion of the real root of 2*x^3 - x^2 - x - 1.
%C A358182 This equals r0 + 1/6 where r0 is the real root of y^3 - (7/12)*y - 16/27.
%C A358182 The other roots of 2*x^3 - x^2 - x - 1 are (1 + w1*(64 + 3*sqrt(417))^(1/3) + w2*(64 - 3*sqrt(417))^(1/3))/6 = -0.3668759642... + 0.5202594388...*i, and its complex conjugate, where w1 = (-1 + sqrt(3)*i)/2 = exp(2*Pi*i/3) and w2 = (-1 - sqrt(3)*i)/2 are the complex conjugate roots of x^3 - 1.
%C A358182 Using hyperbolic functions these roots are (1 - sqrt(7)*( cosh((1/3)*arccosh((64/49)*sqrt(7))) - sqrt(3)*sinh((1/3)*arccosh((64/49)*sqrt(7)))*i))/6, and its complex conjugate.
%F A358182 r = (1 + (64 + 3*sqrt(417))^(1/3) + 7*(64 + 3*sqrt(417))^(-1/3))/6.
%F A358182 r = (1 + (64 + 3*sqrt(417))^(1/3) + (64 - 3*sqrt(417))^(1/3))/6.
%F A358182 r = (1 + 2*sqrt(7)*cosh((1/3)*arccosh((64/49)*sqrt(7))))/6.
%F A358182 r = (1/6) + (4/3)*Hyper2F1([-1/6,1/3],[1/2],3753/4096). - _Gerry Martens_, Nov 08 2022
%e A358182 1.23375192852825878819094337767939303519112723753118649423200988702753759...
%t A358182 RealDigits[x /. FindRoot[2*x^3 - x^2 - x - 1, {x, 1}, WorkingPrecision -> 120]][[1]] (* _Amiram Eldar_, Nov 08 2022 *)
%Y A358182 Cf. A358181, A358183.
%K A358182 nonn,cons,easy
%O A358182 1,2
%A A358182 _Wolfdieter Lang_, Nov 07 2022