关键词: 等差级数, 反平均数, 对偶集

Abstract:

For each integer k≥3, an anti-average k-set  is a set with k nonnegative integers that contains zero and has no three terms in arithmetic progression. We wish to find λ*(k)=min{maxS: S is an anti-average k-set} for every integer k≥3. Some properties and bounds of λ*(k) are shown, and the method of constructing larger anti-average sets are provided.

Key words: Arithmetic progression, Anti-average number, Dual set