A198142 - OEIS

%I #5 Mar 30 2012 18:57:54

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

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

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

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

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

%e least x: 0.89291071141777527373996831831704569...

%e greatest x: 3.6923477739279898601828477062994010...

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

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

%t Plot[{f[x], g[x]}, {x, -1, 4}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, 0.89, 0.90}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198142 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 3.6, 3.7}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198143 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 21 2011