An effective additive basis for the integers
\textit{P. Erdös} [Acta Sci. Math. 15, 255-259 (1954; Zbl 0057.03901)] proved by probabilistic means the existence of a set \(E\) of integers such that the number \(r(n)\) of representations of \(n\) as a sum of two elements of \(E\) satisfies \(c \log n < r(n) < C \log n\). Here an effective construction of such a set is given. The decision to include or exclude \(n\) depends on certain conditional probabilities, whose definition is motivated by Erdös' proof. The procedure produces the elements of \(E\) one by one and the time requires to find all elements up to \(n\) is polynomial in \(n\).
scientific article; zbMATH DE number 810276