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Decimal expansion of least x>0 satisfying x^2+2x+4=tan(x).
2

%I #6 Feb 07 2025 16:44:06

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

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

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

%N Decimal expansion of least x>0 satisfying x^2+2x+4=tan(x).

%C See A200338 for a guide to related sequences. The Mathematica program includes a graph.

%e x=1.460813052223051503419242663379060072493247910...

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

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

%t Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200349 *)

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 16 2011