A198823 - OEIS

%I #5 Mar 30 2012 18:57:56

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

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

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

%N Decimal expansion of x>0 satisfying x^2-2*cos(x)=3.

%C See A198755 for a guide to related sequences.  The Mathematica program includes a graph.

%e x=1.672441304873529513432960452089401997380126680...

%t a = 1; b = -2; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A198823 *)

%Y Cf. A198755.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 30 2011