Integer Sets of Large Harmonic Sum Which Avoid Long Arithmetic Progressions
Alexander Walker
Published: 2022/3/11
Abstract
We give conditions under which certain digit-restricted integer sets avoid $k$-term arithmetic progressions. These sets and their harmonic sums can be computed efficiently. Through large-scale search, we identify integer sets avoiding arithmetic progressions of length 4 and 10 whose harmonic sums exceed earlier "greedy" constructions.