Let N be the set of all nonnegative integers. For a set A⊆N, let R(A,n) denote the number of solutions (a,a′) of a+a′=n with a,a′∈A. The well known Erdős–Turán conjecture says that if R(A,n)⩾1 for all integers n⩾0, then R(A,n) is unbounded. In this Note, the following result is proved: There is a set A⊆N such that R(A,n)⩾1 for all integers n⩾0 and the set of n with R(A,n)=2 has density one.