A note on the lower bound of representation functions

For a set A of nonnegative integers, let R2(A,n) denote the number of solutions to n = a + a′ with a,a′∈ A, a < a′. Let A0 be the Thue–Morse sequence and B0 = ℕ ∖ A0. Let A ⊂ ℕ and N be a positive ...