IMO 1988 LL FRG16

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

IMO 1988 LL FRG16

Origin: FRG

Problem

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