\(B_2\)-sequences and the distinct distance constant (Q1570086)

Let \(1<a_1<a_2< \cdots \) be the consecutive terms of a sequence \(A\) of positive integers. The sequence \(A\) is said to be a \(B_2\)-sequence if all differences \(a_i-a_j\), \(i<j\) are distinct. The authors show that \(2.1600383<d<2.2473\), where \(d\) is the maximum over all \(B_2\)-sequences of the sum \(\sum (1/a_i)\).