Logic is about using deductions to reason about a thing. For example, in sudoku, "If I write a 5 in this cell then the column will contain two 5s. Therefore, this cell can't contain a 5."

Completing sequences of numbers like:

Q: What comes next? 2,3,5,7,11,...

A: 13, it's a list of primes

isn't about logical deduction at all. If anything it's about inference, but I'm probably classify it under pattern matching or something similar. In some sense these problems are meaningless. You could also answer the previous question with

A: -302, the list is the sequence {2,3,5,7,11,-302,5903,pi,....}

and no one can argue with your claim beyond "That's not what I/the author had in mind."

To get better at such things you just need to collect examples. Maybe look at http://oeis.org/Seis.html