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%I #5 Mar 30 2012 18:57:58
%S 1,3,9,6,9,4,8,6,8,3,5,4,5,6,8,4,7,7,2,3,5,2,8,6,3,5,7,9,4,6,5,2,6,8,
%T 2,1,3,9,8,0,4,3,6,8,9,7,5,9,2,7,1,4,1,0,6,1,4,0,9,5,0,0,9,7,9,8,5,7,
%U 9,4,3,9,4,6,9,5,5,3,7,2,4,5,5,0,3,7,8,5,0,4,7,9,5,3,7,9,7,3,8
%N Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=sin(x).
%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -3.6417365104232030891568017121916889194744...
%e greatest: 1.39694868354568477235286357946526821398...
%t a = 1; b = -4; c = 1;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -3.7, -3.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199737 least root *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.39, 1.40}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199738 greatest root *)
%Y Cf. A199597.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 09 2011
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