cp's OEIS Frontend

A199619 Decimal expansion of least x>0 satisfying x^2+4*x*cos(x)=4*sin(x).

%I A199619 #8 Feb 08 2025 10:14:00
%S A199619 8,0,0,0,5,3,3,4,2,6,2,7,4,1,5,7,5,9,3,6,8,5,9,0,2,7,9,9,0,8,9,3,3,2,
%T A199619 1,9,6,3,2,4,4,6,5,3,4,4,8,6,4,6,6,6,1,1,0,4,6,2,1,6,6,9,1,9,5,3,4,1,
%U A199619 3,1,1,0,2,7,7,5,0,4,3,4,1,5,9,6,8,4,1,0,1,2,2,2,9,0,1,5,2,7,6
%N A199619 Decimal expansion of least x>0 satisfying x^2+4*x*cos(x)=4*sin(x).
%C A199619 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199619 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199619 least: 0.80005334262741575936859027990893321963...
%e A199619 greatest:  3.4528998885329277803363008378649838...
%t A199619 a = 1; b = 4; c = 4;
%t A199619 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199619 Plot[{f[x], g[x]}, {x, -.5, 4}, {AxesOrigin -> {0, 0}}]
%t A199619 r = x /. FindRoot[f[x] == g[x], {x, .8, .81}, WorkingPrecision -> 110]
%t A199619 RealDigits[r]  (* A199619, least pos root *)
%t A199619 r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
%t A199619 RealDigits[r]  (* A199620, greatest of 3 roots *)
%Y A199619 Cf. A199597.
%K A199619 nonn,cons
%O A199619 0,1
%A A199619 _Clark Kimberling_, Nov 08 2011