Puzzle

The merchant bought 3-Seedo and 5-Seedo stamps. He proved to himself that he could put together combinations of these two denominations to equal any postage amount required in Seedonia.

Here is his proof:

• The minimum postage in Seedonia is 8 Seedos, which can be made with a 5-Seedo stamp and a 3-Seedo stamp.
• For any postage amount greater than 8, there are two possibilities:
  • It includes a 5-Seedo stamp, or if it doesn’t,
  • it includes at least three 3-Seedo stamps.
    
    • If it includes a 5, he can replace it with two 3s to get the next highest amount.
    • If it includes three 3s, he can replace them with two 5s to get the next highest amount.

In all cases where the postage is at least 8 Seedos, the next highest amount can be made by using one of these two replacements. So it is possible to reach any amount of 8 or more using just 3s and 5s.

Can you come up with other combinations that will work?