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 A201417 Decimal expansion of greatest x satisfying 7*x^2 = sec(x) and 0 < x < Pi. 3

%I

%S 1,5,0,7,9,2,8,7,9,5,3,8,0,0,9,8,2,6,6,5,6,7,8,9,9,9,9,4,0,7,0,9,9,1,

%T 4,1,3,3,9,9,6,3,0,1,1,4,6,2,2,2,1,0,4,1,8,0,3,0,5,4,5,7,3,5,2,6,3,9,

%U 4,0,3,2,6,3,3,9,6,3,2,6,5,4,9,7,2,1,7,5,5,1,3,4,9,7,3,7,6,4,3

%N Decimal expansion of greatest 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 1,2

%A _Clark Kimberling_, Dec 01 2011

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)