cp's OEIS Frontend

A199610 Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=3*sin(x).

%I A199610 #8 Feb 08 2025 10:14:35
%S A199610 3,0,6,5,6,2,0,7,6,0,3,3,6,8,5,8,5,6,1,8,6,7,4,5,7,5,5,2,8,5,0,8,2,1,
%T A199610 3,2,5,0,6,5,4,0,2,0,6,8,2,0,1,7,0,6,2,6,3,9,9,4,5,6,9,0,5,4,3,3,1,2,
%U A199610 5,4,8,2,7,3,8,3,4,7,4,3,0,4,4,5,7,0,8,1,7,8,0,0,8,7,6,1,4,1,1
%N A199610 Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=3*sin(x).
%C A199610 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199610 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199610 least: 1.14225640224474011004461587823586435251534483...
%e A199610 greatest:  3.0656207603368585618674575528508213250654...
%t A199610 a = 1; b = 3; c = 3;
%t A199610 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199610 Plot[{f[x], g[x]}, {x, -1, 4}, {AxesOrigin -> {0, 0}}]
%t A199610 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A199610 RealDigits[r]  (* A199609, least of 3 roots *)
%t A199610 r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
%t A199610 RealDigits[r]  (* A199610, greatest of 3 roots *)
%Y A199610 Cf. A199597.
%K A199610 nonn,cons
%O A199610 1,1
%A A199610 _Clark Kimberling_, Nov 08 2011