A single on; ` thorn electron outside an (N-1)-electron atomic core is bound as long as Z > Z(c) = N - 1. A conjecture is examined, according to which the quantum defect of the outermost electron satisfies lim(Z -> Zc)delta(n,l) (Z) = N-l, where N-l is the number of occupied or partially occupied orbitals with angular momentum quantum number l within the (N-1)-electron core. Specifically, the 3s quantum defect is inspected for the different occupancies of the n 1/4 1 and n = 2 shells. The conjecture is found to hold in all the cases considered. (C) 2018 Elsevier B. V. All rights reserved.