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A201527 Decimal expansion of least x satisfying 9*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201527 #10 Jan 30 2025 15:43:04
%S A201527 4,8,6,6,3,6,5,1,3,4,4,2,8,2,8,7,9,6,4,1,5,0,1,0,6,8,8,8,7,7,4,0,5,3,
%T A201527 0,6,1,5,3,8,3,1,1,0,2,8,3,9,7,3,3,6,9,2,6,7,4,2,5,4,7,1,3,2,8,8,0,9,
%U A201527 9,8,8,9,2,5,7,8,6,4,7,1,9,3,7,2,7,8,9,1,4,0,6,4,1,4,5,6,3,3,9
%N A201527 Decimal expansion of least x satisfying 9*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201527 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201527 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201527 least:  0.4866365134428287964150106888774053061...
%e A201527 greatest: 1.52027247650615034595984357679438306...
%t A201527 a = 9; c = -1;
%t A201527 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201527 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201527 r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
%t A201527 RealDigits[r]   (* A201527 *)
%t A201527 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201527 RealDigits[r]   (* A201528 *)
%Y A201527 Cf. A201397.
%K A201527 nonn,cons
%O A201527 0,1
%A A201527 _Clark Kimberling_, Dec 02 2011