The answer is 8.  Here's why I say that.

One way to look at it is to take the integers starting with 2:

 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, ...

and replace the multiples of 5 by 3's

 2,  3,  4,  3,  6,  7,  8,  9,  3, 11, 12, 13, 14,  3, 16, ...


Or it could be 'replace every 4th one by 3'

 2,  3,  4,  3,  6,  7,  8,  3, 10, 11, 12,  3, 14, 15, 16, ...

Or it could be 'replace every 4th number by 1 less than the preceding number:

 2,  3,  4,  3,  6,  7,  8,  7, 10, 11, 12, 11, 14, 15, 16, ...

So there is no way to determine which pattern they follow.  However in every
case above the next number after 7 was 8.  So regardless of the pattern, the
answer would be 8.

Edwin