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A201406 Decimal expansion of least x satisfying 2*x^2 = sec(x) and 0 < x < Pi.

%I A201406 #10 Jan 30 2025 15:34:49
%S A201406 8,9,2,8,7,4,3,0,6,0,5,8,9,6,1,1,2,4,4,4,7,3,7,1,9,6,9,0,1,8,6,7,7,5,
%T A201406 1,4,6,0,1,9,5,6,8,6,1,1,9,6,7,9,4,0,3,4,0,4,7,1,7,4,5,4,5,0,3,7,8,9,
%U A201406 5,6,9,1,0,3,2,5,6,6,5,7,7,2,1,7,1,8,2,0,4,1,5,3,4,7,5,5,1,0,7
%N A201406 Decimal expansion of least x satisfying 2*x^2 = sec(x) and 0 < x < Pi.
%C A201406 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201406 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201406 least:  0.892874306058961124447371969018677514...
%e A201406 greatest: 1.2390826209275819187151092399019855...
%t A201406 a = 2; c = 0;
%t A201406 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201406 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201406 r = x /. FindRoot[f[x] == g[x], {x, .8, 1}, WorkingPrecision -> 110]
%t A201406 RealDigits[r]   (* A201406 *)
%t A201406 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A201406 RealDigits[r]   (* A201407 *)
%Y A201406 Cf. A201397.
%K A201406 nonn,cons
%O A201406 0,1
%A A201406 _Clark Kimberling_, Dec 01 2011