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%I #10 Aug 09 2021 14:14:32
%S 1,5,2,2,8,6,7,1,7,6,6,7,7,9,3,0,0,5,7,3,8,6,9,0,7,4,7,3,3,4,5,6,2,6,
%T 0,8,2,0,5,8,9,8,9,5,1,0,6,3,5,7,4,9,4,3,0,9,9,6,1,5,5,5,4,8,9,2,2,9,
%U 8,2,8,2,9,3,9,5,7,9,4,8,6,7,6,8,2,6,7,3,7,9,2,5,3,2,6,0,1,7,9,9
%N Decimal expansion of greatest x satisfying 9*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: 0.3435193844487517285157937916054768...
%e greatest: 1.52286717667793005738690747334562...
%t a = 9; 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] (* A201420 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201421 *)
%Y Cf. A201397.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Dec 02 2011
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