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A201412 Decimal expansion of least x satisfying 5*x^2 = sec(x) and 0 < x < Pi.

%I A201412 #10 Jan 30 2025 15:36:23
%S A201412 4,7,4,1,2,7,6,9,0,4,2,0,7,7,5,4,1,5,9,3,4,7,4,8,9,3,8,5,6,9,5,5,1,5,
%T A201412 3,8,4,3,4,8,7,2,9,2,8,5,7,5,9,9,9,6,5,6,9,8,3,4,8,5,2,3,4,5,7,3,5,4,
%U A201412 6,4,1,8,0,4,0,1,6,8,9,7,3,3,5,6,1,0,0,2,8,4,3,3,3,8,1,2,4,9,6
%N A201412 Decimal expansion of least x satisfying 5*x^2 = sec(x) and 0 < x < Pi.
%C A201412 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201412 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201412 least:  0.474127690420775415934748938569551538434...
%e A201412 greatest: 1.4792710652904107931042853415537602633...
%t A201412 a = 5; c = 0;
%t A201412 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201412 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201412 r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
%t A201412 RealDigits[r]     (* A201412 *)
%t A201412 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201412 RealDigits[r]    (* A201413 *)
%Y A201412 Cf. A201397.
%K A201412 nonn,cons
%O A201412 0,1
%A A201412 _Clark Kimberling_, Dec 01 2011