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

%I #6 Feb 07 2025 16:44:05

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

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

%U 0,9,2,4,8,8,1,6,1,5,6,5,2,8,8,4,4,1,9,3,6,8,6,8,2,5,6,9,8,2,8

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

%C See A198414 for a guide to related sequences. The Mathematica program includes a graph.

%e x=2.674098087050680851553639389992305676666...

%t a = 1; b = -2; c = 4;

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

%t Plot[{f[x], g[x]}, {x, -.2, 3}]

%t r = x /. FindRoot[f[x] == g[x], {x, 2.67, 2.68}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198430 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 25 2011