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

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

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

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

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

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

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

%e x=3.0350408224380488468671230709648237806015888...

%t a = 1; b = -3; c = 1;

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

%t Plot[{f[x], g[x]}, {x, -.2, 3.5}]

%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198431 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 25 2011