cp's OEIS Frontend

A200625 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 3 = tan(x) and 0 < x < Pi/2.

%I A200625 #10 Jan 30 2025 13:17:05
%S A200625 1,4,3,4,4,3,6,7,9,8,5,3,1,0,6,4,8,8,2,7,1,8,8,6,4,3,5,1,3,5,4,3,3,5,
%T A200625 8,5,0,3,4,3,9,6,6,8,1,5,1,2,5,3,6,8,1,7,1,8,4,8,5,3,0,2,3,6,4,7,1,1,
%U A200625 6,6,0,5,2,5,8,3,9,9,2,6,4,1,9,5,5,1,8,5,9,7,6,8,1,3,6,1,6,6,6
%N A200625 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 3 = tan(x) and 0 < x < Pi/2.
%C A200625 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200625 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200625 lesser:  0.9325170518642294819498571898931399897...
%e A200625 greater: 1.4344367985310648827188643513543358503...
%t A200625 a = 5; c = 3;
%t A200625 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200625 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200625 r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
%t A200625 RealDigits[r]   (* A200624 *)
%t A200625 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200625 RealDigits[r]   (* A200625 *)
%Y A200625 Cf. A200614.
%K A200625 nonn,cons
%O A200625 1,2
%A A200625 _Clark Kimberling_, Nov 20 2011