login

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

Decimal expansion of least x having x^2-4x=-2*cos(x).
3

%I #5 Mar 30 2012 18:57:53

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

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

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

%N Decimal expansion of least x having x^2-4x=-2*cos(x).

%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.

%e least x: 0.50130475545480646339369035756819...

%e greatest x: 4.222749528794927324484249676610...

%t a = 1; b = -4; c = -2;

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

%t Plot[{f[x], g[x]}, {x, 0, 5}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198100 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 4.2, 4.3}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198101 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 21 2011