Hello,

The given series is 3, 7, 11, 13, ...

3 -->(+4)--> 7 -->(+4)--> 11 -->(+2, it is half of 4)--> 13 -->(+2 ,following the trend)--> 15 --> (+1, it is half of 2)--> 16

This is the only relation that I was able to make out. There might be others as well. You can look for relations like: addition, subtraction, squares etc.

Hope this helps.
Thanks.