On the Erdős-diameter of sets

Let δ(n) denote the minimum diameter of a set of n points in the plane in which any two positive distances, if they are different, differ by at least one. Erdős conjectured that for n sufficiently big we have δ(n) = n − 1, the extremal configuration being n equidistant points on a line. In this note we prove an asymptotic version of this conjecture for the special case of sets which lie in a parallel half-strip.