cp's OEIS Frontend

A199732 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=4*sin(x).

%I A199732 #8 Feb 08 2025 22:12:09
%S A199732 1,7,1,7,7,6,1,7,0,1,5,5,9,1,4,6,7,3,7,9,4,6,5,4,6,9,3,7,6,8,3,0,8,4,
%T A199732 0,1,0,8,3,6,6,9,6,2,7,3,2,6,4,6,5,7,0,5,3,1,8,2,8,1,3,5,5,1,1,2,3,7,
%U A199732 5,0,4,2,0,1,0,9,6,6,9,3,3,1,2,8,9,7,5,5,1,6,9,0,7,5,6,1,0,1,3
%N A199732 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=4*sin(x).
%C A199732 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199732 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199732 least: -3.80284270062359171640437975188554983520...
%e A199732 greatest:  1.71776170155914673794654693768308401...
%t A199732 a = 1; b = -4; c = 4;
%t A199732 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199732 Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
%t A199732 r = x /. FindRoot[f[x] == g[x], {x, -3.9, -3.8}, WorkingPrecision -> 110]
%t A199732 RealDigits[r]   (* A199731 least of 4 roots *)
%t A199732 r = x /. FindRoot[f[x] == g[x], {x, 1.71, 1.72}, WorkingPrecision -> 110]
%t A199732 RealDigits[r]   (* A199732 greatest of 4 roots *)
%Y A199732 Cf. A199597.
%K A199732 nonn,cons
%O A199732 1,2
%A A199732 _Clark Kimberling_, Nov 09 2011