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A201519 Decimal expansion of least x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201519 #11 Jan 30 2025 15:41:45
%S A201519 6,7,5,4,8,2,9,0,8,1,1,3,7,2,4,2,2,8,0,1,5,1,7,8,8,5,8,1,9,0,8,2,7,3,
%T A201519 1,5,9,4,1,0,7,4,0,1,2,5,4,4,0,8,8,0,7,9,6,4,4,8,5,0,8,0,4,5,2,7,2,3,
%U A201519 7,1,5,8,0,3,2,5,1,7,3,9,1,3,5,7,5,5,1,1,7,5,3,3,0,3,5,5,2,1,1
%N A201519 Decimal expansion of least x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201519 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201519 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201519 least:  0.675482908113724228015178858190...
%e A201519 greatest: 1.4683742920332829376554687815...
%t A201519 a = 5; c = -1;
%t A201519 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201519 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201519 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A201519 RealDigits[r]   (* A201519 *)
%t A201519 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201519 RealDigits[r]   (* A201520 *)
%Y A201519 Cf. A201397.
%K A201519 nonn,cons
%O A201519 0,1
%A A201519 _Clark Kimberling_, Dec 02 2011