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%I #8 Apr 10 2021 08:07:13
%S 3,6,5,8,6,8,4,4,2,1,8,1,0,4,6,9,0,9,4,4,4,8,8,7,9,5,0,9,1,8,0,3,6,6,
%T 4,6,0,8,1,3,8,4,5,6,4,5,7,0,2,3,0,7,3,9,7,3,1,2,9,8,0,3,0,0,6,6,9,3,
%U 5,0,8,6,2,0,3,6,5,3,7,8,9,3,1,2,1,4,9,7,5,2,2,9,3,9,9,0,4,2,3
%N Decimal expansion of least 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 0,1
%A _Clark Kimberling_, Dec 01 2011