cp's OEIS Frontend

A201524 Decimal expansion of greatest x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201524 #10 Jan 30 2025 15:42:01
%S A201524 1,5,0,3,2,6,2,1,5,2,1,3,1,4,9,3,0,9,9,9,1,9,0,7,9,9,0,7,5,2,0,0,8,3,
%T A201524 0,8,2,9,0,8,3,4,3,1,7,1,5,6,2,7,8,2,9,3,8,3,2,1,0,3,3,2,1,4,8,8,7,2,
%U A201524 7,4,9,7,2,3,3,7,5,1,4,2,4,9,8,0,0,9,9,4,8,7,2,9,9,6,6,2,0,5,6
%N A201524 Decimal expansion of greatest x satisfying 7*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201524 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201524 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201524 least:  0.557895175779035299832869736313873...
%e A201524 greatest: 1.5032621521314930999190799075200...
%t A201524 a = 7; c = -1;
%t A201524 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201524 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201524 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201524 RealDigits[r]   (* A201523 *)
%t A201524 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201524 RealDigits[r]   (* A201524 *)
%Y A201524 Cf. A201397.
%K A201524 nonn,cons
%O A201524 1,2
%A A201524 _Clark Kimberling_, Dec 02 2011