
complement of sets
I have infinitely many sets, like:
$\displaystyle $a_l:= ]2 \cdot k \cdot 3^l + 3^l; 2 \cdot k \cdot 3^l + 2 \cdot 3^l [$$, where $\displaystyle $l$$ is positive integer, and $\displaystyle $k$$ is a positive integer. I wrote a computer program which filtered out those elements which was not in the $\displaystyle $a_l$$ sets.
The result is:
{6,7,8,9
18,19,20,21
24,25,26,27
54,55,56,57
60,61,62,63
72,73,74,75
78,79,80,81}
.... and so on. I observed this sequence has a period (12,6,30,6). But I have no idea how to prove it. Can you help me? Thanks.
update: k is also a positive integer