A201530 - OEIS

%I #8 Apr 09 2021 19:16:20

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

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

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

%N Decimal expansion of greatest x satisfying 10*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:  0.4600006985794904216969349833844460938634...

%e greatest: 1.52590577141056614542926620695066975318...

%t a = 10; 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, .4, .5}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201529 *)

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

%t RealDigits[r]   (* A201530 *)

%Y Cf. A201397.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 02 2011