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

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

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

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

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

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

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

%e x=1.68184524494501231093262862021941994235640...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 1.68, 1.69}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198549 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 26 2011