Some extensions of additive properties of general sequences

Let A = { a 1 , a 2 ,…}( a 1 < a 2 < …) be an infinite sequence of positive integers. Let k ≥ 2 be a fixed integer and denote by R k ( n ) the number of solutions of . Erdős, Sárközy and Sós studied the boundness of | R 2 ( n + 1) − R 2 ( n )| and the monotonicity property of R 2 ( n ). In this paper, we extend some results to k >...