An effective additive basis for the integers

We give an algorithm for the enumeration of a set E of nonnegative integers with the property that each nonnegative integer x can be written as a sum of two elements of E in at least C1 log x and at most C2 log x ways, where C1, C2 are positive constants. Such a set is called a basis and its existence has been established by Erdős. Our algorithm takes time polynomial in n to enumerate all elements of E not greater than n. We accomplish this by derandomizing a probabilistic proof which is slightly different than that given by Erdős.