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A201517 Decimal expansion of least x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201517 #11 Jan 30 2025 15:40:21
%S A201517 7,7,4,4,2,7,2,5,7,0,7,9,8,9,3,6,2,3,2,5,7,0,2,9,0,0,9,0,0,0,6,2,4,5,
%T A201517 6,3,9,8,5,9,1,3,6,7,7,8,3,5,0,7,9,2,6,8,7,8,4,2,5,9,1,6,0,5,0,5,9,2,
%U A201517 7,3,0,3,6,8,2,5,8,1,2,4,6,4,8,7,2,7,2,4,4,6,5,7,4,2,9,1,6,4,1
%N A201517 Decimal expansion of least x satisfying 4*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201517 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201517 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201517 least:  0.774427257079893623257029009000...
%e A201517 greatest: 1.4313635500690391357640449937...
%t A201517 a = 4; c = -1;
%t A201517 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201517 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201517 r = x /. FindRoot[f[x] == g[x], {x, .7, .8}, WorkingPrecision -> 110]
%t A201517 RealDigits[r]   (* A201517 *)
%t A201517 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201517 RealDigits[r]   (* A201518 *)
%Y A201517 Cf. A201397.
%K A201517 nonn,cons
%O A201517 0,1
%A A201517 _Clark Kimberling_, Dec 02 2011