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%I #8 Apr 10 2021 08:07:01
%S 3,9,3,2,7,3,8,2,7,3,2,8,8,4,1,5,0,3,8,3,2,4,5,2,0,5,7,2,0,6,2,5,3,4,
%T 2,6,5,9,1,4,5,2,1,7,7,2,0,3,0,3,2,2,0,5,9,1,8,2,9,7,1,9,8,6,8,9,1,8,
%U 8,7,1,5,2,9,8,6,0,8,6,3,5,3,9,4,1,4,6,2,8,9,1,1,5,9,4,9,3,2,6
%N Decimal expansion of least x satisfying 7*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: 0.39327382732884150383245205720625342659...
%e greatest: 1.507928795380098266567899994070991413...
%t a = 7; 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] (* A201416 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201417 *)
%Y Cf. A201397.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 01 2011
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