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A201410 Decimal expansion of least x satisfying 4*x^2 = sec(x) and 0 < x < Pi.

%I A201410 #12 Jan 30 2025 15:36:15
%S A201410 5,3,9,8,6,1,0,8,3,9,1,2,7,7,8,4,4,3,6,3,0,6,7,3,7,3,2,7,3,2,2,8,0,7,
%T A201410 1,4,8,0,6,2,4,1,1,2,0,9,8,1,6,0,0,5,5,4,0,8,2,8,9,8,5,4,6,1,6,0,8,1,
%U A201410 4,4,0,2,1,2,2,0,9,8,5,5,6,0,8,2,7,8,7,3,2,0,6,5,3,0,5,9,8,3,0
%N A201410 Decimal expansion of least x satisfying 4*x^2 = sec(x) and 0 < x < Pi.
%C A201410 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201410 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201410 least:  0.53986108391277844363067373273228071480624...
%e A201410 greatest: 1.451925722123287999446946604502079960054...
%t A201410 a = 4; c = 0;
%t A201410 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201410 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201410 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201410 RealDigits[r]    (* A201410 *)
%t A201410 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201410 RealDigits[r]    (* A201411 *)
%Y A201410 Cf. A201397.
%K A201410 nonn,cons
%O A201410 0,1
%A A201410 _Clark Kimberling_, Dec 01 2011