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Decimal expansion of least x>0 satisfying 6-x^2=tan(x).
2

%I #10 Jan 30 2025 13:41:20

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

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

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

%N Decimal expansion of least x>0 satisfying 6-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 1.3376284727280084884715783884188457087587110...

%t a = -1; c = 6;

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

%t RealDigits[r] (* A200690 *)

%Y Cf. A200338.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 21 2011