A200683 - OEIS

%I #10 Jan 30 2025 13:35:12

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

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

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

%N Decimal expansion of the lesser of two values of x satisfying 4*x^2 = tan(x) and 0 < x < Pi/2.

%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 lesser:  0.2555899667465678034714126335398146...

%e greater: 1.4529161609165145187427486875904483...

%t a = 4; c = 0;

%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](* A200683 *)

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

%t RealDigits[r](* A200684 *)

%Y Cf. A200614.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 20 2011