%I #5 Mar 30 2012 18:57:53
%S 1,0,2,5,1,1,9,1,1,1,9,9,2,4,2,9,0,1,4,8,4,6,1,9,8,5,7,5,0,0,5,7,8,3,
%T 2,5,1,5,3,5,3,8,3,5,2,1,4,6,7,3,4,8,9,4,2,1,5,9,2,7,4,5,5,9,7,6,7,4,
%U 9,2,7,9,1,0,2,1,2,6,0,6,9,3,1,4,3,6,1,5,9,8,8,0,8,4,5,3,6,1,0
%N Decimal expansion of x>0 having x^2+x=4*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e negative: -1.42077677317100524932506694166184882...
%e positive: 1.025119111992429014846198575005783251...
%t a = 1; b = 1; c = 4;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -2, 1.5}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.4}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A197813 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, 1, 1.1}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A197814 *)
%Y Cf. A197737.
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Oct 20 2011
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