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A201523 Decimal expansion of least x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201523 #10 Jan 30 2025 15:41:55
%S A201523 5,5,7,8,9,5,1,7,5,7,7,9,0,3,5,2,9,9,8,3,2,8,6,9,7,3,6,3,1,3,8,7,3,7,
%T A201523 9,8,3,9,2,7,5,7,3,9,8,4,7,4,4,1,5,3,6,3,8,0,6,8,1,1,8,6,2,6,2,0,8,9,
%U A201523 0,3,8,8,6,4,1,1,8,6,4,3,1,4,9,8,1,9,8,7,9,0,5,1,2,7,0,9,2,2,0
%N A201523 Decimal expansion of least x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201523 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201523 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201523 least:  0.557895175779035299832869736313873...
%e A201523 greatest: 1.5032621521314930999190799075200...
%t A201523 a = 7; c = -1;
%t A201523 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201523 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201523 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201523 RealDigits[r]   (* A201523 *)
%t A201523 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201523 RealDigits[r]   (* A201524 *)
%Y A201523 Cf. A201397.
%K A201523 nonn,cons
%O A201523 0,1
%A A201523 _Clark Kimberling_, Dec 02 2011