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+3x=4*cos(x).
3

%I #7 Aug 09 2021 07:37:35

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

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

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

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

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

%e least x: -2.072191302711809327379682290027003...

%e greatest x: 0.7657264429205407174831010492394...

%t a = 1; b = 3; c = 4;

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

%t Plot[{f[x], g[x]}, {x, -3, 1}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -2.1, -2.9}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198108 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .76, .77}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198109 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 21 2011