IMO 1988 LL FRG17

Show that if n runs through all positive integers, f(n) =

IMO 1988 LL FRG17

Origin: FRG

Problem

Show that if n runs through all positive integers, f(n) = / n + \sqrt 3n + 1/2 runs through all positive integers skipping the terms of the sequence an =  n2+2n  .