B2-sequences and the distinct distance constant

A sequence of positive integers 1 < α1 < α2 < … with the property that all differences αj − αi, i < j are distinct is called a B2-sequence. Denote by DDC (distinct difference constant) the maximum over all possible B2-sequences of the sum ∑(1/αi). Previously known upper and lower bounds for the DDC are 2.1597 < DDC < 2.374. We have estimated the following sharper bounds on DDC: 2.1600383 < DDC < 2.2473. We have further proved that any B2-sequence which achieves the maximum reciprocal sum must start with the terms 1,2,4.