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%I #5 Mar 30 2012 18:57:57
%S 1,3,6,0,6,7,2,7,7,2,5,1,3,7,9,7,2,1,5,2,2,8,6,0,2,7,4,8,7,3,7,9,9,2,
%T 5,8,8,0,9,6,8,6,2,8,0,8,5,7,6,1,8,0,9,4,7,4,5,8,1,9,1,7,7,1,9,7,1,2,
%U 0,7,6,2,0,8,6,5,3,3,7,9,2,3,5,3,1,4,1,9,0,8,0,8,3,3,8,2,9,4,0
%N Decimal expansion of least x satisfying x^2+3*x*cos(x)=1.
%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -1.3606727725137972152286027487379925...
%e greatest: 3.27746466341373058734587727791083...
%t a = 1; b = 3; c = 1;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199182 least of four roots *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.27, 3.28}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199183 greatest of four roots *)
%Y Cf. A199170.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 04 2011