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Math Help - complement of sets

  1. #1
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    complement of sets

    I have infinitely many sets, like:

    $a_l:= ]2 \cdot k \cdot 3^l  + 3^l; 2 \cdot k \cdot 3^l  + 2 \cdot 3^l [$, where $l$ is positive integer, and $k$ is a positive integer. I wrote a computer program which filtered out those elements which was not in the $a_l$ 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
    Last edited by Ben92; February 7th 2011 at 07:32 AM.
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