A set of numbers is defined as a1=1, a2=2, a3=3, and a number n belongs to this set if it can be written as a unique sum of three distinct members of this set e.g. a4=6, a5=9, a6=10, a7=11, a8=12 but 13, 14, 15, 16, 17 do not belong to this set. Is this set of numbers finite or infinite? Prove your claim.
I've been trying to solve this question by contradiction. So I assume that the set is finite. I have no idea how to proceed. can anyone give me a hint?