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 A199270 #13 Feb 07 2025 16:44:05
%S A199270 3,8,1,7,4,8,4,2,0,9,9,2,9,8,5,9,5,7,9,1,8,5,2,1,6,1,1,8,2,3,4,8,6,6,
%T A199270 4,5,5,9,3,3,4,1,8,5,5,0,7,6,7,1,7,8,3,1,6,0,6,3,2,9,9,1,9,0,3,7,7,0,
%U A199270 9,1,5,4,0,8,1,6,0,9,0,2,1,1,1,5,5,3,2,0,8,5,2,6,3,3,7,3,0,1,6
%N A199270 Decimal expansion of x > 0 satisfying 2*x^2 + 2*x*cos(x) = 1.
%C A199270 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199270 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199270 negative: -1.017240798342455566560350070545346176017411...
%e A199270 positive: 0.381748420992985957918521611823486645593341...
%t A199270 a = 2; b = 2; c = 1;
%t A199270 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199270 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199270 r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
%t A199270 RealDigits[r] (* A199269 *)
%t A199270 r = x /. FindRoot[f[x] == g[x], {x, .38, .39}, WorkingPrecision -> 110]
%t A199270 RealDigits[r] (* A199270 *)
%Y A199270 Cf. A199170, A199269.
%K A199270 nonn,cons
%O A199270 0,1
%A A199270 _Clark Kimberling_, Nov 04 2011
%E A199270 a(84) onwards corrected by _Georg Fischer_, Aug 03 2021