cp's OEIS Frontend

A200624 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 3 = tan(x) and 0 < x < Pi/2.

%I A200624 #10 Jan 30 2025 13:17:01
%S A200624 9,3,2,5,1,7,0,5,1,8,6,4,2,2,9,4,8,1,9,4,9,8,5,7,1,8,9,8,9,3,1,3,9,9,
%T A200624 8,9,7,6,4,9,1,7,3,6,7,7,6,1,8,0,6,4,5,2,3,9,0,8,8,9,6,8,9,1,4,2,8,6,
%U A200624 3,2,4,8,6,6,9,2,4,5,1,5,4,5,3,2,2,7,7,0,3,8,6,5,7,0,6,4,3,7,6
%N A200624 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 3 = tan(x) and 0 < x < Pi/2.
%C A200624 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200624 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200624 lesser:  0.9325170518642294819498571898931399897649173...
%e A200624 greater: 1.43443679853106488271886435135433585034396681...
%t A200624 a = 5; c = 3;
%t A200624 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200624 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200624 r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
%t A200624 RealDigits[r]    (* A200624 *)
%t A200624 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200624 RealDigits[r]   (* A200625 *)
%Y A200624 Cf. A200614.
%K A200624 nonn,cons
%O A200624 0,1
%A A200624 _Clark Kimberling_, Nov 20 2011