Chen's conjecture and its generalization

Let l (1), l (2), ..., l (g) be even integers and x be a sufficiently large number. In this paper, the authors prove that the number of positive odd integers k a parts per thousand currency sign x such that (k + l (1))(2), (k + l (2))(2), ..., (k + l (g) )(2) can not be expressed as 2 (n) + p (alpha) is at least c(g)x, where p is an odd prime and the constant c(g) depends only on g.