An Upper Bound for B2[2] Sequences

n = b + a, a ≤ b, a, b ∈ A. n = b + a, a < b, a, b ∈ A. n = b− a, a < b, a, b ∈ A. We say that a sequence of integers A belongs to the class of B2[g] sequences if r(n) ≤ g for any integer n. To find B2[g] sequences as dense as possible is a standard problem in additive number theory ([2],[5],[6],[7]). We define F (N, g) = max{|A|, A ⊂ [1, N ], A ∈ B2[g]}. One is interested in finding precise bounds of F (N, g) For finite B2[g] sequences we have the following simple argument. Let A ⊂ [1, N ], be A a B2[g] sequence. Then (|A|+ 1 2 ) = 2N ∑