cp's OEIS Frontend

A201413 Decimal expansion of greatest x satisfying 5*x^2 = sec(x) and 0 < x < Pi.

%I A201413 #12 Jan 30 2025 15:36:26
%S A201413 1,4,7,9,2,7,1,0,6,5,2,9,0,4,1,0,7,9,3,1,0,4,2,8,5,3,4,1,5,5,3,7,6,0,
%T A201413 2,6,3,3,4,3,0,8,8,6,0,3,8,0,1,4,0,0,2,7,0,9,5,6,1,9,9,2,7,1,9,5,9,0,
%U A201413 7,5,2,5,0,0,9,1,6,6,2,6,7,9,0,3,1,8,7,1,0,0,1,7,8,4,7,3,9,2,1,8,7
%N A201413 Decimal expansion of greatest x satisfying 5*x^2 = sec(x) and 0 < x < Pi.
%C A201413 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201413 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201413 least:  0.474127690420775415934748938569551538434...
%e A201413 greatest: 1.4792710652904107931042853415537602633...
%t A201413 a = 5; c = 0;
%t A201413 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201413 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201413 r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
%t A201413 RealDigits[r]    (* A201412 *)
%t A201413 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A201413 RealDigits[r]    (* A201413 *)
%Y A201413 Cf. A201397.
%K A201413 nonn,cons
%O A201413 1,2
%A A201413 _Clark Kimberling_, Dec 01 2011