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Decimal expansion of least x>0 satisfying 1-10*x^2=tan(x).
1

%I #8 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of least x>0 satisfying 1-10*x^2=tan(x).

%C See A200614 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 0.2691096712789465665224706482190210588356212...

%t a = -10; c = 1;

%t f[x_] := a*x^2 + 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, .2, .3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200710 *)

%Y Cf. A200338.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 21 2011