Some Sequence Puzzles

Here are some sequences I made up.  They're not really math problems.  Instead, they just require some problem-solving skills.  The first one is the easiest.  The other two have about the same difficulty.

For each of these, find the next three terms and how the sequence is defined.

First one:
1, 1, 3, 4, 5, 7, 7, 10, 9, ...

Second one:
6, 9, 15, 21, 33, 39, ...

Third one:
1, 8, 7, 4, 5, 6, ...
Hint: solve the following sequence first.
1, 4, 9, 6, 5, 6, ...

Have fun!  I hope this stretches your mind a bit!

Since many of you will probably be lazy and just look for the answer, I'll encode them in Base64 encoding so that you'll have to decode them.  Don't worry, though, it's easy.  Just use this online Base64 translator.


Answers (super-small text so it takes up less space because you're not actually going to try and read it anyway... are you?):
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