Counting numerical sets with no small atoms

A numerical set S with Frobenius number g is a set of integers with min(S)=0 and max(Z−S)=g, and its atom monoid is . Let γg be the ratio of the number of numerical sets S having A(S)={0}∪(g,∞) divided by the total number of numerical sets with Frobenius number g. We show that the sequence {γg} is decreasing and converges to a number γ_∞≈.4844 (with accuracy to within .0050). We also examine the singularities of the generating function for {γg}. Parallel results are obtained for the ratio of the number of symmetric numerical sets S with A(S)={0}∪(g,∞) by the number of symmetric numerical sets with Frobenius number g. These results yield information regarding the asymptotic behavior of the number of finite additive 2-bases.