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A201409 Decimal expansion of greatest x satisfying 3*x^2 = sec(x) and 0 < x < Pi.

%I A201409 #10 Jan 30 2025 15:36:09
%S A201409 1,3,9,9,8,6,4,1,1,9,4,4,6,0,6,4,0,6,7,2,2,9,6,3,9,5,0,5,1,8,3,6,1,0,
%T A201409 3,7,3,9,4,1,7,8,5,0,3,3,6,2,5,3,2,6,3,4,4,2,0,4,1,4,9,8,8,7,0,4,9,5,
%U A201409 8,0,2,7,1,7,3,5,1,0,6,0,0,3,3,5,7,9,7,0,2,0,5,7,8,1,6,5,9,1,9
%N A201409 Decimal expansion of greatest x satisfying 3*x^2 = sec(x) and 0 < x < Pi.
%C A201409 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201409 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201409 least:  0.6461374540628972972901679159101125226952859...
%e A201409 greatest: 1.39986411944606406722963950518361037394178...
%t A201409 a = 3; c = 0;
%t A201409 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201409 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201409 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A201409 RealDigits[r]    (* A201408 *)
%t A201409 r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
%t A201409 RealDigits[r]    (* A201409 *)
%Y A201409 Cf. A201397.
%K A201409 nonn,cons
%O A201409 1,2
%A A201409 _Clark Kimberling_, Dec 01 2011