A201411 - OEIS

%I #8 Apr 10 2021 08:06:26

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

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

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

%N Decimal expansion of greatest x satisfying 4*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:  0.53986108391277844363067373273228071480624...

%e greatest: 1.451925722123287999446946604502079960054...

%t a = 4; 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, .5, .6}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201410 *)

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

%t RealDigits[r]    (* A201411 *)

%Y Cf. A201397.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 01 2011