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A201423 Decimal expansion of greatest x satisfying 10*x^2 = sec(x) and 0 < x < Pi.

%I A201423 #12 Jan 30 2025 15:40:14
%S A201423 1,5,2,7,9,4,9,8,9,4,6,9,8,6,1,4,4,1,9,6,4,9,2,4,4,7,5,2,4,6,8,0,1,9,
%T A201423 8,4,7,4,3,0,5,4,9,8,4,6,9,8,8,5,8,3,4,6,0,2,2,7,6,4,3,7,4,6,8,8,0,0,
%U A201423 1,0,6,3,7,2,5,6,8,1,3,5,5,6,2,2,9,3,9,5,4,0,8,6,8,8,8,6,0,4,2,5
%N A201423 Decimal expansion of greatest x satisfying 10*x^2 = sec(x) and 0 < x < Pi.
%C A201423 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201423 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201423 least:  0.3248357625526726343272168905918357...
%e A201423 greatest: 1.52794989469861441964924475246801...
%t A201423 a = 10; c = 0;
%t A201423 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201423 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201423 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A201423 RealDigits[r]    (* A201422 *)
%t A201423 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201423 RealDigits[r]    (* A201423 *)
%Y A201423 Cf. A201397.
%K A201423 nonn,cons
%O A201423 1,2
%A A201423 _Clark Kimberling_, Dec 02 2011