A198111 - OEIS

%I #7 Aug 09 2021 07:38:06

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

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

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

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

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

%e x=0.940349965355053888229393687614968909...

%t a = 2; b = 0; c = 3;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 0.94, 0.95}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198111 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 21 2011