cp's OEIS Frontend

A199731 Decimal expansion of least x satisfying x^2-4*x*cos(x)=4*sin(x).

%I A199731 #9 Feb 08 2025 13:24:09
%S A199731 3,8,0,2,8,4,2,7,0,0,6,2,3,5,9,1,7,1,6,4,0,4,3,7,9,7,5,1,8,8,5,5,4,9,
%T A199731 8,3,5,2,0,1,6,2,3,0,2,9,5,9,6,2,4,3,7,0,5,5,8,8,6,2,4,0,5,4,1,0,7,3,
%U A199731 1,2,1,0,7,7,9,5,1,0,7,4,3,9,3,3,6,0,5,3,6,4,5,4,5,6,8,5,4,5,7
%N A199731 Decimal expansion of least x satisfying x^2-4*x*cos(x)=4*sin(x).
%C A199731 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199731 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199731 least: -3.80284270062359171640437975188554983520...
%e A199731 greatest:  1.71776170155914673794654693768308401...
%t A199731 a = 1; b = -4; c = 4;
%t A199731 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199731 Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
%t A199731 r = x /. FindRoot[f[x] == g[x], {x, -3.9, -3.8}, WorkingPrecision -> 110]
%t A199731 RealDigits[r]   (* A199731 least of 4 roots *)
%t A199731 r = x /. FindRoot[f[x] == g[x], {x, 1.71, 1.72}, WorkingPrecision -> 110]
%t A199731 RealDigits[r]   (* A199732 greatest of 4 roots *)
%Y A199731 Cf. A199597.
%K A199731 nonn,cons
%O A199731 1,1
%A A199731 _Clark Kimberling_, Nov 09 2011