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

%I #9 Feb 07 2025 16:44:06

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

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

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

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

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

%e x=1.30747760030134992121693507169004808...

%t a = 1; b = 0; c = 2;

%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, 1.3, 1.4}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200339 *)

%o (PARI) solve(x=1,1.5,x^2+2-tan(x)) \\ _Charles R Greathouse IV_, Mar 23 2022

%Y Cf. A200338.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 16 2011