On a problem of Erdös in additive number theory
A well known result of \textit{P. Erdös} [Proc. Am. Math. Soc. 5, 847-853 (1954; Zbl 0056.27001)] and \textit{G. Lorentz} [Proc. Am. Math. Soc. 5, 838-841 (1954; Zbl 0056.03902)] asserts the existence of sets \(A\) of integers with i) \(\# \{a \leq x:a\in A\} \ll \log^2 x\); ii) every sufficiently large integer \(n\) can be written as \(n=p+a\) with \(p\) prime and \(a\in A\). The author shows that there exists a set \(A\) with i)' \(\# \{a\leq x:a \in A\} \ll h(x) \log x\log \log x\), \(h(x)\) tending to \(\infty\) arbitrarily slowly; ii)' almost all integers \(n\) can be written as \(n=p + a\) with \(p\) prime and \(a\in A\).
scientific article; zbMATH DE number 913837