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Idiot World's Math Godeek Test

It's easy to see patterns where no patterns exist.. or do they?
Just get the next number in the sequence. It should be as easy as 1, 2, ..., err, what's the next number?

Good luck.. you might need it (or you can cheat and Google)
Google
Be patient, don't panic! (42?)

e.g.: 1, 2, 3,
Freebies
1, 2, 4, 8, 16,
0, 1, 1, 2, 3, 5,
0, 1, 3, 6, 10,
3, 1, 4, 1, 5, 9, 2
2, 3, 5, 7,
1, 2, 6, 24, 120,
Slightly Tricky
1, 2, 5, 10, 17,
1, 11, 21, 1211, 111221,
59, 154, 605, 1111,
1, 4, 27, 256,
Math comes in
125, 376, 188, 94, 47
1, 2, 6, 20, 70,
1, 1, 3, 11, 45, 197,
1, 1, 5, 61, 1385,
6, 28, 496, 8128
1, 5, 14, 30, 55,
1, 2, 5, 15, 52,
1, 2, 5, 14, 42,
Outside the box
4, 8, 15, 16, 23,
14, 23, 28, 33, 42,
5, 9, 14, 27, 29, 54, 59,


You currently have
0
correct. Go for it! (Connect 4?)

"God made the positive integers; all else is the work of man."
Leopold Kronecker

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