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%I #10 Aug 10 2021 09:38:05
%S 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 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 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 Decimal expansion of greatest x satisfying 8*x^2 = sec(x) and 0 < x < Pi.
%C See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%e least: 0.365868442181046909444887950918036646081...
%e greatest: 1.5164098481119355896362189407751970807...
%t a = 8; c = 0;
%t f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201418 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201419 *)
%Y Cf. A201397.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Dec 01 2011
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