cp's OEIS Frontend

A199735 Decimal expansion of least x satisfying x^2-4*x*cos(x)=2*sin(x).

%I A199735 #8 Feb 08 2025 13:26:39
%S A199735 3,6,9,2,2,1,4,2,4,5,4,3,5,8,4,0,4,6,1,1,2,1,0,1,6,8,2,9,3,7,2,6,8,7,
%T A199735 5,3,8,5,0,8,6,7,2,6,7,2,8,8,7,7,5,4,8,6,6,1,1,3,9,7,7,6,9,2,3,2,9,4,
%U A199735 3,2,8,2,7,9,0,8,1,8,4,0,2,9,2,5,4,9,9,1,9,7,2,2,4,2,6,7,1,7,3
%N A199735 Decimal expansion of least x satisfying x^2-4*x*cos(x)=2*sin(x).
%C A199735 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199735 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199735 least: -3.69221424543584046112101682937268753850...
%e A199735 greatest:  1.519514926470401221585705162098148990...
%t A199735 a = 1; b = -4; c = 2;
%t A199735 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199735 Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
%t A199735 r = x /. FindRoot[f[x] == g[x], {x, -3.7, -3.6}, WorkingPrecision -> 110]
%t A199735 RealDigits[r]   (* A199735 least root *)
%t A199735 r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
%t A199735 RealDigits[r]   (* A199736 greatest root *)
%Y A199735 Cf. A199597.
%K A199735 nonn,cons
%O A199735 1,1
%A A199735 _Clark Kimberling_, Nov 09 2011