Sums of perturbed sequences of integers
Let \(\{a_ n\}^{\infty}_{n=1}\) be an increasing sequence of nonnegative integers. Given a set P of integers, a sequence \(\{b_ n\}^{\infty}_{n=1}\) is called a P-perturbation of A if \(b_ n-a_ n\in P\) for all n. The authors investigate the stability of the notion of an asymptotic basis and a subbasis of order h under ``small'' perturbations. For instance, to every increasing sequence A of nonnegative integers, there exists a \(\{0,1,2\}\)-perturbation of A which is not a subbasis of order 2. Then the authors prove a result related to Goldbach conjecture. Namely, that there exists a \(\{-2,0,2\}\)-perturbation of the set of odd primes which is not a subbasis of order 2 and the number of perturbed primes less than n is \(\ll n/\log n \log \log n.\)
stability of basis properties under small perturbations
scientific article; zbMATH DE number 4073116