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

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

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

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

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

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

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

%e x=0.7284682393569907683615322781499074705250953...

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

%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, .72, .73}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198564 *)

%Y Cf. A198414.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 26 2011