A199663 - OEIS

%I #8 Feb 08 2025 22:14:04

%S 3,3,9,6,3,1,2,6,0,3,1,9,1,7,8,8,7,5,3,6,7,4,6,6,6,6,2,4,7,8,8,0,8,0,

%T 5,3,1,0,7,7,8,8,4,2,3,0,7,5,8,5,8,3,6,7,9,4,4,2,5,8,9,3,3,9,1,4,2,6,

%U 9,0,4,8,9,8,1,0,0,4,4,8,4,3,5,4,8,0,0,1,3,6,6,3,6,7,4,9,2,5,2

%N Decimal expansion of x>0 satisfying 3*x^2+x*cos(x)=2*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 0.3396312603191788753674666624788080...

%t a = 3; b = 1; c = 2;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, .33, .34}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A199663 *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 09 2011