ILL 1988 Problem 17

If $n$ runs through all the positive integers, then $f(n) = \left \lfloor n + \sqrt {3n} + \frac {1}{2} \right \rfloor$ runs through all positive integers skipping the terms of the sequence $a_n = \left \lfloor \frac {n^2 + 2n}{3} \right \rfloor$ .