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A201414 Decimal expansion of least x satisfying 6*x^2 = sec(x) and 0 < x < Pi.

%I A201414 #10 Jan 30 2025 15:37:12
%S A201414 4,2,8,0,0,8,9,5,0,1,0,0,4,1,0,9,7,0,0,2,7,3,9,3,4,7,7,6,9,0,6,9,1,8,
%T A201414 0,6,5,9,8,8,9,2,9,5,9,2,8,9,4,0,5,9,6,1,9,0,8,4,8,8,6,2,3,6,8,0,3,1,
%U A201414 4,0,1,3,7,6,6,8,3,2,6,6,7,1,4,7,2,0,8,4,8,5,8,1,4,7,9,9,9,8,5
%N A201414 Decimal expansion of least x satisfying 6*x^2 = sec(x) and 0 < x < Pi.
%C A201414 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201414 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201414 least:  0.42800895010041097002739347769069180659...
%e A201414 greatest: 1.496285048607652953479229041712424469...
%t A201414 a = 6; c = 0;
%t A201414 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201414 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201414 r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
%t A201414 RealDigits[r]    (* A201414 *)
%t A201414 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201414 RealDigits[r]    (* A201415 *)
%Y A201414 Cf. A201397.
%K A201414 nonn,cons
%O A201414 0,1
%A A201414 _Clark Kimberling_, Dec 01 2011