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A200626 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 4 = tan(x) and 0 < x < Pi/2.

%I A200626 #10 Jan 30 2025 13:17:08
%S A200626 1,0,8,6,2,4,8,3,0,7,3,7,2,3,5,1,4,9,3,0,5,1,6,5,3,7,4,7,0,2,5,7,9,0,
%T A200626 1,3,0,2,1,1,1,2,7,3,5,5,4,3,6,3,1,5,1,1,7,1,8,9,4,2,5,9,8,4,9,7,6,9,
%U A200626 4,5,4,7,8,5,2,6,3,5,8,1,9,0,8,9,9,5,8,4,4,2,6,6,5,2,0,8,5,4,8
%N A200626 Decimal expansion of the lesser of two values of x satisfying 5*x^2 - 4 = tan(x) and 0 < x < Pi/2.
%C A200626 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200626 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200626 lesser:  1.0862483073723514930516537470257901302111...
%e A200626 greater: 1.4001025553369417418319593715715854730538...
%t A200626 a = 5; c = 4;
%t A200626 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200626 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200626 r = x /. FindRoot[f[x] == g[x], {x, .9, 1.0}, WorkingPrecision -> 110]
%t A200626 RealDigits[r]   (* A200626 *)
%t A200626 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200626 RealDigits[r]   (* A200627 *)
%Y A200626 Cf. A200614.
%K A200626 nonn,cons
%O A200626 1,3
%A A200626 _Clark Kimberling_, Nov 20 2011