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 A201407 Decimal expansion of greatest x satisfying 2*x^2=sec(x) and 0

%I

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

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

%U 5,6,7,6,8,9,1,6,6,6,7,5,4,8,4,3,7,7,8,8,0,8,7,6,7,7,9,7,5,9,0

%N Decimal expansion of greatest x satisfying 2*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: 0.892874306058961124447371969018677514...

%e greatest: 1.2390826209275819187151092399019855...

%t a = 2; 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, .8, 1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201406 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201407 *)

%Y Cf. A201397.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 01 2011

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Last modified June 19 11:28 EDT 2013. Contains 226404 sequences.