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A201420 Decimal expansion of least x satisfying 9*x^2 = sec(x) and 0 < x < Pi.

%I A201420 #10 Jan 30 2025 15:38:42
%S A201420 3,4,3,5,1,9,3,8,4,4,4,8,7,5,1,7,2,8,5,1,5,7,9,3,7,9,1,6,0,5,4,7,6,8,
%T A201420 6,0,1,4,4,8,5,9,7,4,9,4,9,4,2,1,8,9,6,5,0,9,4,4,1,5,8,8,5,3,7,2,3,4,
%U A201420 6,8,9,3,0,4,9,5,5,9,8,9,1,9,6,8,4,5,8,0,9,1,9,1,9,6,2,4,0,8,6
%N A201420 Decimal expansion of least x satisfying 9*x^2 = sec(x) and 0 < x < Pi.
%C A201420 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201420 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201420 least:  0.3435193844487517285157937916054768...
%e A201420 greatest: 1.52286717667793005738690747334562...
%t A201420 a = 9; c = 0;
%t A201420 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201420 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201420 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A201420 RealDigits[r]     (* A201420 *)
%t A201420 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201420 RealDigits[r]    (* A201421 *)
%Y A201420 Cf. A201397.
%K A201420 nonn,cons
%O A201420 0,1
%A A201420 _Clark Kimberling_, Dec 02 2011