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A201529 Decimal expansion of least x satisfying 10*x^2 - 1 = sec(x) and 0 < x < Pi.

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