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A201518 Decimal expansion of greatest x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201518 #11 Jan 30 2025 15:40:27
%S A201518 1,4,3,1,3,6,3,5,5,0,0,6,9,0,3,9,1,3,5,7,6,4,0,4,4,9,9,3,7,8,2,7,5,4,
%T A201518 2,1,3,0,4,1,2,3,9,5,6,8,1,7,9,9,6,4,5,3,6,5,1,5,2,4,6,6,6,2,8,0,3,0,
%U A201518 0,3,3,6,4,7,5,9,5,6,4,3,9,0,3,8,9,5,2,1,6,2,8,8,2,5,4,7,9,9,4
%N A201518 Decimal expansion of greatest x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201518 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201518 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201518 least:  0.774427257079893623257029009000...
%e A201518 greatest: 1.4313635500690391357640449937...
%t A201518 a = 4; c = -1;
%t A201518 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201518 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201518 r = x /. FindRoot[f[x] == g[x], {x, .7, .8}, WorkingPrecision -> 110]
%t A201518 RealDigits[r]   (* A201517 *)
%t A201518 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201518 RealDigits[r]   (* A201518 *)
%Y A201518 Cf. A201397.
%K A201518 nonn,cons
%O A201518 1,2
%A A201518 _Clark Kimberling_, Dec 02 2011