cp's OEIS Frontend

A200684 Decimal expansion of the greater of two values of x satisfying 4*x^2 = tan(x) and 0 < x < Pi/2.

%I A200684 #12 Jan 30 2025 13:34:51
%S A200684 1,4,5,2,9,1,6,1,6,0,9,1,6,5,1,4,5,1,8,7,4,2,7,4,8,6,8,7,5,9,0,4,4,8,
%T A200684 3,2,3,2,4,0,2,2,5,9,9,9,0,3,2,5,0,9,5,1,4,9,7,6,4,6,3,1,3,0,5,3,3,6,
%U A200684 2,8,3,7,1,6,6,5,5,6,8,6,0,7,3,1,9,9,2,4,8,3,1,1,1,7,1,5,3,1,2
%N A200684 Decimal expansion of the greater of two values of x satisfying 4*x^2 = tan(x) and 0 < x < Pi/2.
%C A200684 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200684 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200684 lesser:  0.25558996674656780347141263353981468112668...
%e A200684 greater: 1.45291616091651451874274868759044832324022...
%t A200684 a = 4; c = 0;
%t A200684 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200684 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200684 r = x /. FindRoot[f[x] == g[x], {x, .2, .3}, WorkingPrecision -> 110]
%t A200684 RealDigits[r](* A200683 *)
%t A200684 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200684 RealDigits[r](* A200684 *)
%Y A200684 Cf. A200614, A200683.
%K A200684 nonn,cons
%O A200684 1,2
%A A200684 _Clark Kimberling_, Nov 20 2011