cp's OEIS Frontend

A201520 Decimal expansion of greatest x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201520 #12 Jan 30 2025 15:41:38
%S A201520 1,4,6,8,3,7,4,2,9,2,0,3,3,2,8,2,9,3,7,6,5,5,4,6,8,7,8,1,5,8,0,5,4,6,
%T A201520 6,9,4,6,9,2,0,5,9,7,4,2,8,6,1,4,1,7,5,6,0,3,2,9,3,8,4,9,7,7,5,5,7,5,
%U A201520 6,9,6,9,3,6,9,2,3,4,0,7,1,4,5,9,7,9,0,3,1,1,3,5,3,2,8,4,7,8,5
%N A201520 Decimal expansion of greatest x satisfying 5*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201520 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201520 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201520 least: 0.675482908113724228015178858190...
%e A201520 greatest: 1.4683742920332829376554687815...
%t A201520 a = 5; c = -1;
%t A201520 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201520 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201520 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A201520 RealDigits[r]   (* A201519 *)
%t A201520 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201520 RealDigits[r]   (* A201520 *)
%Y A201520 Cf. A201397.
%K A201520 nonn,cons
%O A201520 1,2
%A A201520 _Clark Kimberling_, Dec 02 2011