C_3: 0 _________1/9; 2/9 _________ 1/3; 2/3 _________7/9; 8/9 _________ 1.

C_4: 0 ___ 1/27; 2/27 ___ 1/9; 2/9 ___ 7/27; 8/27 ___1/3; 2/3 ___ 19/27; 20/27 ___ 7/9; 8/9 ___ 25/27; 26/27 ___ 1.

C_5: 0 _ 1/81; 2/81 _ 1/27; 2/27 _ 7/81; 8/81 _ 1/9; 2/9 _ 19/81; 20/81 _ 7/27; 8/27 _ 25/81; 26/81 _ 1/3; 2/3 _ 55/81; 56/81 _ 19/27; 20/27 _ 61/81; 62/81 _ 7/9; 8/9 _ 73/81; 74/81 _ 25/27; 26/27 _ 79/81; 80/81 _ 1.

\frac{1}{3}

is in the Cantor set (it's a point on the end of an interval so is kept).

$\frac{4}{9}$ is not in the Cantor set: it's removed when going from $C_{1}$ to $C_{2}$ .

$\frac{3}{81} = \frac{1}{27}$ is in the Cantor set (it's a point on the end of an interval).

$\frac{4}{81}$ is not in the Cantor set: it's removed when going from $C_{3}$ to $C_{4}$ .