%I #8 Apr 09 2021 22:53:53

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

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

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

%N Decimal expansion of least x satisfying 7*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: 0.557895175779035299832869736313873...

%e greatest: 1.5032621521314930999190799075200...

%t a = 7; 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, .5, .6}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201523 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201524 *)

%Y Cf. A201397.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 02 2011