A199609 - OEIS

%I #8 Feb 08 2025 10:08:44

%S 1,1,4,2,2,5,6,4,0,2,2,4,4,7,4,0,1,1,0,0,4,4,6,1,5,8,7,8,2,3,5,8,6,4,

%T 3,5,2,5,1,5,3,4,4,8,3,4,4,5,7,6,4,5,7,4,8,1,0,1,7,4,4,4,6,2,4,3,1,6,

%U 6,5,1,6,7,4,3,3,7,0,9,4,5,1,6,0,9,7,2,6,6,3,4,9,3,4,7,6,2,6,6

%N Decimal expansion of least x>0 satisfying x^2+3*x*cos(x)=3*sin(x).

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least: 1.14225640224474011004461587823586435251534483...

%e greatest:  3.0656207603368585618674575528508213250654...

%t a = 1; b = 3; c = 3;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -1, 4}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199609, least x>0 of 3 roots *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199610, greatest of 3 roots *)

%Y Cf. A199597.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 08 2011