Question 886373
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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,  <font color="red">3</font>,  6,  7,  8,  9,  <font color="red">3</font>, 11, 12, 13, 14,  <font color="red">3</font>, 16, ...


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

 2,  3,  4,  <font color="red">3</font>,  6,  7,  8,  <font color="red">3</font>, 10, 11, 12,  <font color="red">3</font>, 14, 15, 16, ...

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

 2,  3,  4,  <font color="red">3</font>,  6,  7,  8,  <font color="red">7</font>, 10, 11, 12, <font color="red">11</font>, 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</pre>