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 A199590 #20 Oct 27 2023 11:14:23 %S A199590 2,5,7,7,7,2,8,0,1,0,3,1,4,4,0,8,4,4,7,2,9,4,4,9,3,9,7,2,7,0,6,3,5,8, %T A199590 2,2,7,0,8,9,4,4,1,2,5,7,0,0,9,7,7,3,1,9,7,8,2,3,1,4,6,3,9,3,9,5,8,0, %U A199590 8,6,4,4,5,7,6,7,3,0,5,3,7,0,8,5,8,2,4,9,9,8,0,0,3,1,0,1,5,7,2,3 %N A199590 Decimal expansion (unsigned) of the greatest root of 6x^3 + 18x^2 + 12x + 2 = 0. %C A199590 If the side lengths of a quadrilateral form a harmonic progression in the ratio 1 : 1/(1+d) : 1/(1+2d) : 1/(1+3d) where d is the common difference between the denominators of the harmonic progression, then the triangle inequality condition requires that d be in the range f < d < g, where f = -0.257772801... and is the greatest root of the equation: 2 + 12d + 18d^2 + 6d^3 = 0. The value of g is given in A199589. %H A199590 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a> %F A199590 sqrt(4/3)*sin(Pi*2/9) - 1. - _Charles R Greathouse IV_, Nov 10 2011 %e A199590 -0.257772801031440844729449397270635822708944125700977319782314639395808... %t A199590 N[Reduce[2+12d+18d^2+6d^3==0, d], 100] %o A199590 (PARI) real(polroots(6*x^3+18*x^2+12*x+2)[3]) \\ _Charles R Greathouse IV_, Nov 10 2011 %o A199590 (PARI) polrootsreal(6*x^3-18*x^2+12*x-2)[1] \\ _Charles R Greathouse IV_, Oct 27 2023 %Y A199590 Cf. A010503, A199220, A199221, A199589. %K A199590 nonn,cons %O A199590 0,1 %A A199590 _Frank M Jackson_, Nov 08 2011 %E A199590 a(99) corrected by _Sean A. Irvine_, Jul 25 2021