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A201408 Decimal expansion of least x satisfying 3*x^2 = sec(x) and 0 < x < Pi.

%I A201408 #10 Jan 30 2025 15:36:07
%S A201408 6,4,6,1,3,7,4,5,4,0,6,2,8,9,7,2,9,7,2,9,0,1,6,7,9,1,5,9,1,0,1,1,2,5,
%T A201408 2,2,6,9,5,2,8,5,9,6,3,3,4,5,9,2,3,2,0,0,9,7,0,9,4,5,7,1,1,4,2,5,7,7,
%U A201408 6,9,1,3,5,1,6,4,1,3,0,4,9,6,1,4,6,0,3,0,6,0,9,0,3,4,7,3,2,1,7
%N A201408 Decimal expansion of least x satisfying 3*x^2 = sec(x) and 0 < x < Pi.
%C A201408 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201408 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201408 least:  0.6461374540628972972901679159101125226952859...
%e A201408 greatest: 1.39986411944606406722963950518361037394178...
%t A201408 a = 3; c = 0;
%t A201408 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201408 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201408 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A201408 RealDigits[r]    (* A201408 *)
%t A201408 r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
%t A201408 RealDigits[r]    (* A201409 *)
%Y A201408 Cf. A201397.
%K A201408 nonn,cons
%O A201408 0,1
%A A201408 _Clark Kimberling_, Dec 01 2011