cp's OEIS Frontend

A201416 Decimal expansion of least x satisfying 7*x^2 = sec(x) and 0 < x < Pi.

%I A201416 #10 Jan 30 2025 15:39:07
%S A201416 3,9,3,2,7,3,8,2,7,3,2,8,8,4,1,5,0,3,8,3,2,4,5,2,0,5,7,2,0,6,2,5,3,4,
%T A201416 2,6,5,9,1,4,5,2,1,7,7,2,0,3,0,3,2,2,0,5,9,1,8,2,9,7,1,9,8,6,8,9,1,8,
%U A201416 8,7,1,5,2,9,8,6,0,8,6,3,5,3,9,4,1,4,6,2,8,9,1,1,5,9,4,9,3,2,6
%N A201416 Decimal expansion of least x satisfying 7*x^2 = sec(x) and 0 < x < Pi.
%C A201416 See A201397 for a guide to related sequences. The Mathematica program includes a graph.
%H A201416 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201416 least:  0.39327382732884150383245205720625342659...
%e A201416 greatest: 1.507928795380098266567899994070991413...
%t A201416 a = 7; c = 0;
%t A201416 f[x_] := a*x^2 + c; g[x_] := Sec[x]
%t A201416 Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A201416 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A201416 RealDigits[r]    (* A201416 *)
%t A201416 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A201416 RealDigits[r]    (* A201417 *)
%Y A201416 Cf. A201397.
%K A201416 nonn,cons
%O A201416 0,1
%A A201416 _Clark Kimberling_, Dec 01 2011