cp's OEIS Frontend

A201411 Decimal expansion of greatest x satisfying 4*x^2 = sec(x) and 0 < x < Pi.

%I A201411 #10 Jan 30 2025 15:36:18
%S A201411 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 A201411 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 A201411 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 A201411 Decimal expansion of greatest x satisfying 4*x^2 = sec(x) and 0 < x < Pi.
%C A201411 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201411 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201411 least:  0.53986108391277844363067373273228071480624...
%e A201411 greatest: 1.451925722123287999446946604502079960054...
%t A201411 a = 4; c = 0;
%t A201411 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201411 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201411 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201411 RealDigits[r]    (* A201410 *)
%t A201411 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201411 RealDigits[r]    (* A201411 *)
%Y A201411 Cf. A201397.
%K A201411 nonn,cons
%O A201411 1,2
%A A201411 _Clark Kimberling_, Dec 01 2011