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A201407 Decimal expansion of greatest x satisfying 2*x^2 = sec(x) and 0 < x < Pi.

%I A201407 #10 Jan 30 2025 15:34:52
%S A201407 1,2,3,9,0,8,2,6,2,0,9,2,7,5,8,1,9,1,8,7,1,5,1,0,9,2,3,9,9,0,1,9,8,5,
%T A201407 5,3,8,0,5,9,7,0,2,3,5,0,1,4,3,6,4,9,1,5,7,2,1,6,0,1,7,3,8,1,6,9,8,5,
%U A201407 5,6,7,6,8,9,1,6,6,6,7,5,4,8,4,3,7,7,8,8,0,8,7,6,7,7,9,7,5,9,0
%N A201407 Decimal expansion of greatest x satisfying 2*x^2 = sec(x) and 0 < x < Pi.
%C A201407 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201407 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201407 least:  0.892874306058961124447371969018677514...
%e A201407 greatest: 1.2390826209275819187151092399019855...
%t A201407 a = 2; c = 0;
%t A201407 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201407 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201407 r = x /. FindRoot[f[x] == g[x], {x, .8, 1}, WorkingPrecision -> 110]
%t A201407 RealDigits[r]   (* A201406 *)
%t A201407 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A201407 RealDigits[r]   (* A201407 *)
%Y A201407 Cf. A201397.
%K A201407 nonn,cons
%O A201407 1,2
%A A201407 _Clark Kimberling_, Dec 01 2011