Problems and results on additive properties of general sequences. II (Q1090363)

Let \(a_1<a_2<\dots\) be an infinite sequence of positive integers and \(R(n)\) be the number of solutions of \(a_i+a_j=n\). In Part I [Pac. J. Math. 118, 347--357 (1985; Zbl 0569.10032)] the authors proved that \(R(n)\) cannot be too regular in the sense \(R(n)=F(n)+o(\sqrt{F(n)})\) cannot hold for ``nice'' functions \(F(n)\). In Part II a probabilistic construction is presented to show that the above result is essentially best possible.