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A201528 Decimal expansion of greatest x satisfying 9*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201528 #10 Jan 30 2025 15:43:07
%S A201528 1,5,2,0,2,7,2,4,7,6,5,0,6,1,5,0,3,4,5,9,5,9,8,4,3,5,7,6,7,9,4,3,8,3,
%T A201528 0,6,3,0,4,2,1,6,3,8,0,6,1,0,2,5,7,5,3,9,3,3,2,7,0,7,3,2,6,4,6,0,7,6,
%U A201528 8,0,7,7,6,2,1,2,1,3,7,2,4,4,6,1,0,5,4,5,3,5,0,0,9,2,6,7,1,0,0
%N A201528 Decimal expansion of greatest x satisfying 9*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201528 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201528 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201528 least:  0.4866365134428287964150106888774053061...
%e A201528 greatest: 1.52027247650615034595984357679438306...
%t A201528 a = 9; c = -1;
%t A201528 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201528 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201528 r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
%t A201528 RealDigits[r]   (* A201527 *)
%t A201528 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201528 RealDigits[r]   (* A201528 *)
%Y A201528 Cf. A201397.
%K A201528 nonn,cons
%O A201528 1,2
%A A201528 _Clark Kimberling_, Dec 02 2011