B-2-sequences and the distinct distance constant

A sequence of positive integers 1 < alpha(1) < alpha(2) < ... with the prop erty that all differences alpha(j) - alpha(i), i < j are distinct is called a B-2-sequence. Denote by DDC (distinct difference constant;) the maximum over all possible B-2-sequences of the sum Sigma(1/(alpha)i). Previously kn own upper and lower bounds for the DDC are 2.1597 < DDC < 2.374. We have es timated the following sharper bounds on DDC: 2.1600383 < DDC < 2.2473. We h ave further proved that any B-2-sequence which achieves the maximum recipro cal sum must start with the terms 1,2,4. (C) 2000 Elsevier Science Ltd. All rights reserved.