A201519 - OEIS

%I #9 Apr 10 2021 02:03:27

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

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

%U 7,1,5,8,0,3,2,5,1,7,3,9,1,3,5,7,5,5,1,1,7,5,3,3,0,3,5,5,2,1,1

%N Decimal expansion of least x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

%C See A201397 for a guide to related sequences. The Mathematica program includes a graph.

%e least:  0.675482908113724228015178858190...

%e greatest: 1.4683742920332829376554687815...

%t a = 5; c = -1;

%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, .6, .7}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201519 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201520 *)

%Y Cf. A201397.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 02 2011