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A201530 Decimal expansion of greatest x satisfying 10*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201530 #10 Jan 30 2025 15:43:14
%S A201530 1,5,2,5,9,0,5,7,7,1,4,1,0,5,6,6,1,4,5,4,2,9,2,6,6,2,0,6,9,5,0,6,6,9,
%T A201530 7,5,3,1,8,6,9,3,5,1,7,0,0,5,3,9,8,0,6,7,9,9,2,9,5,0,3,0,4,6,8,3,6,6,
%U A201530 5,7,8,0,1,2,2,6,5,6,9,5,6,2,7,3,8,9,6,2,2,4,2,2,9,3,4,5,3,4,7
%N A201530 Decimal expansion of greatest x satisfying 10*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201530 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201530 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201530 least:  0.4600006985794904216969349833844460938634...
%e A201530 greatest: 1.52590577141056614542926620695066975318...
%t A201530 a = 10; c = -1;
%t A201530 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201530 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201530 r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
%t A201530 RealDigits[r]   (* A201529 *)
%t A201530 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201530 RealDigits[r]   (* A201530 *)
%Y A201530 Cf. A201397.
%K A201530 nonn,cons
%O A201530 1,2
%A A201530 _Clark Kimberling_, Dec 02 2011