cp's OEIS Frontend

A199618 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=3*sin(x).

%I A199618 #8 Feb 08 2025 10:14:02
%S A199618 3,4,8,2,2,6,7,6,2,4,7,8,6,1,9,3,2,0,9,0,8,6,7,0,3,6,6,7,5,5,7,6,8,0,
%T A199618 3,7,0,7,6,2,6,9,3,1,5,6,9,4,5,6,0,3,6,9,3,8,3,9,7,6,9,9,3,4,9,0,0,4,
%U A199618 8,4,2,1,8,7,6,3,9,8,5,1,0,8,3,9,9,3,9,4,9,6,8,6,4,8,5,8,9,5,7
%N A199618 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=3*sin(x).
%C A199618 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199618 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199618 least: -0.5535433817860336287020344905911816930...
%e A199618 greatest:  3.4822676247861932090867036675576803...
%t A199618 a = 1; b = 4; c = 3;
%t A199618 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199618 Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
%t A199618 r = x /. FindRoot[f[x] == g[x], {x, -.56, -.55}, WorkingPrecision -> 110]
%t A199618 RealDigits[r]  (* A199617, least of 4 roots *)
%t A199618 r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
%t A199618 RealDigits[r]  (* A199618, greatest of 4 roots *)
%Y A199618 Cf. A199597.
%K A199618 nonn,cons
%O A199618 0,1
%A A199618 _Clark Kimberling_, Nov 08 2011