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Decimal expansion of x>0 having 4*x^2=cos(x).
2

%I #6 Mar 30 2012 18:57:54

%S 4,7,1,8,8,7,6,4,8,2,4,7,7,8,4,3,4,4,7,0,6,5,7,4,4,4,7,6,8,6,5,6,7,7,

%T 7,7,4,8,1,0,2,9,8,7,6,0,7,2,2,7,0,7,9,4,3,0,5,8,8,1,6,6,0,0,5,9,1,2,

%U 4,9,8,8,7,3,0,2,3,6,4,2,9,5,8,6,7,0,8,2,4,3,9,5,3,5,4,3,3,8,4

%N Decimal expansion of x>0 having 4*x^2=cos(x).

%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.471887648247784344706574447686567777...

%t a = 4; b = 0; c = 1;

%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]

%t Plot[{f[x], g[x]}, {x, -1, 1}]

%t r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198347 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011