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

%I #7 Feb 07 2025 16:44:06

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

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

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

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

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

%e x=1.438371935323166343024711233387578921848390...

%t a = 1; b = 1; 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] (* A200345 *)

%Y Cf. A200338.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 16 2011