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A201419 Decimal expansion of greatest x satisfying 8*x^2 = sec(x) and 0 < x < Pi.

%I A201419 #12 Jan 30 2025 15:38:38
%S A201419 1,5,1,6,4,0,9,8,4,8,1,1,1,9,3,5,5,8,9,6,3,6,2,1,8,9,4,0,7,7,5,1,9,7,
%T A201419 0,8,0,7,6,6,7,9,5,6,1,1,8,2,4,4,3,0,6,3,4,7,6,0,8,6,1,0,3,9,9,9,5,2,
%U A201419 4,0,4,5,1,7,0,0,0,1,2,8,9,8,1,1,2,1,9,0,3,9,7,8,2,8,9,3,9,6,8
%N A201419 Decimal expansion of greatest x satisfying 8*x^2 = sec(x) and 0 < x < Pi.
%C A201419 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201419 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201419 least:  0.365868442181046909444887950918036646081...
%e A201419 greatest: 1.5164098481119355896362189407751970807...
%t A201419 a = 8; c = 0;
%t A201419 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201419 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201419 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A201419 RealDigits[r]    (* A201418 *)
%t A201419 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201419 RealDigits[r]    (* A201419 *)
%Y A201419 Cf. A201397.
%K A201419 nonn,cons
%O A201419 1,2
%A A201419 _Clark Kimberling_, Dec 01 2011