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

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

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

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

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

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

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

%e x=2.488425259653566017487498494936179715450...

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

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

%t Plot[{f[x], g[x]}, {x, -.2, 2.5}]

%t r = x /. FindRoot[f[x] == g[x], {x, 2.48, 2.49}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198428 *)

%Y Cf. A198414.

%K nonn,cons,changed

%O 1,1

%A _Clark Kimberling_, Oct 25 2011