cp's OEIS Frontend

A201515 Decimal expansion of least x satisfying 3*x^2 - 1 = sec(x) and 0 < x < Pi.

%I A201515 #11 Jan 30 2025 15:40:17
%S A201515 9,5,3,5,3,9,0,9,7,5,4,9,9,1,4,6,8,9,6,6,7,2,7,0,6,9,5,3,7,2,3,7,8,2,
%T A201515 2,7,4,3,3,6,0,9,6,5,6,0,5,1,5,1,6,0,6,8,0,6,9,6,9,6,0,1,9,7,9,7,3,5,
%U A201515 6,7,6,1,0,2,2,9,8,0,9,1,3,6,4,7,8,7,6,9,4,7,8,2,7,9,5,7,4,5,7
%N A201515 Decimal expansion of least x satisfying 3*x^2 - 1 = sec(x) and 0 < x < Pi.
%C A201515 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201515 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201515 least:  0.95353909754991468966727069537237822743...
%e A201515 greatest: 1.341430166291259764576080506763614171...
%t A201515 a = 3; c = -1;
%t A201515 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201515 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201515 r = x /. FindRoot[f[x] == g[x], {x, .9, 1}, WorkingPrecision -> 110]
%t A201515 RealDigits[r]  (* A201515 *)
%t A201515 r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.5}, WorkingPrecision -> 110]
%t A201515 RealDigits[r]  (* A201516 *)
%Y A201515 Cf. A201397.
%K A201515 nonn,cons
%O A201515 0,1
%A A201515 _Clark Kimberling_, Dec 02 2011