login
Decimal expansion of x>0 having 3*x^2-x=3*sin(x).
2

%I #6 Feb 07 2025 16:44:05

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

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

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

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

%C See A198414 for a guide to related sequences. The Mathematica program includes a graph.

%e x=1.1327784166780435512983725437241083850697730022...

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

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

%t Plot[{f[x], g[x]}, {x, -.1, 1.5}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.13, 1.14}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198552 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Oct 26 2011