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Decimal expansion of x>0 having 4*x^2=3*sin(x).
2

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

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

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

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

%N Decimal expansion of x>0 having 4*x^2=3*sin(x).

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

%e x=0.691621364625584532007116403137264073...

%t a = 4; b = 0; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -.2, 1}]

%t r = x /. FindRoot[f[x] == g[x], {x, .69, .7}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198504 *)

%Y Cf. A198414.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Oct 25 2011