login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%I #6 Mar 30 2012 18:57:57

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

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

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

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

%C See A199429 for a guide to related sequences. The Mathematica program includes a graph.

%e x=1.09770607306519042940162895829193901300597891048...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 1.08, 1.09}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199503 *)

%Y Cf. A199429.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 07 2011