Asymptotic basis

asymptotic basis of order $k$

A sequence of natural numbers and zero, which as a result of its summation repeated $k$ times yields all sufficiently large natural numbers. The number $k$ is called the order of the asymptotic basis. Thus, the sequence of prime numbers is an asymptotic basis of order 4 (I.M. Vinogradov, 1937); the sequence of cubes of natural numbers is an asymptotic basis of order 7 (Yu.V. Linnik, 1942).