Flibbertigibbet

A Puzzle

What's the next number in this series:

1, 7, 13, 19, 15, 9, 3, 7, 11, 17, 13, 9, __

I have no idea how a person would go about figuring this out, but I'm throwing it out there to see if someone can.

Remind me and I'll tell you the answer later.

Update: My best friend figured it out and there is a pattern. (If you take a few minutes to look at it, you'll see it.)

Here's another one, but try to do the next 4 numbers:

1, 7, 13, 19, 25, 31, 37, 43, 49, 44, 39, __, __, __, __

Bonus points if you can tell me where I got that second pattern.