A199741 - OEIS

%I #12 Jan 12 2025 14:24:34

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

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

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

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

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

%e x=1.0642302228710730261002141143294370961885395132859...

%t a = 2; 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, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.06, 1.07}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A199741 *)

%Y Cf. A199597.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 10 2011

%E Name corrected by _Sean A. Irvine_, Jan 12 2025