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%I #10 Aug 03 2021 14:29:03
%S 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 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 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 Decimal expansion of x > 0 satisfying 2*x^2 + 2*x*cos(x) = 1.
%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%e negative: -1.017240798342455566560350070545346176017411...
%e positive: 0.381748420992985957918521611823486645593341...
%t a = 2; b = 2; c = 1;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199269 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .38, .39}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199270 *)
%Y Cf. A199170, A199269.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 04 2011
%E a(84) onwards corrected by _Georg Fischer_, Aug 03 2021
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