A201526 - OEIS

%I #10 Jan 30 2025 15:43:02

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

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

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

%N Decimal expansion of greatest x satisfying 8*x^2 - 1 = sec(x) and 0 < x < Pi.

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least:  0.518577002201711458253109820417244...

%e greatest: 1.5130057374477490977746930540120...

%t a = 8; 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]   (* A201525 *)

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

%t RealDigits[r]   (* A201526 *)

%Y Cf. A201397.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 02 2011