Erdős Problem #348

For what values of \(0 \leq m < n\) is there a complete sequence \(A = \{a_1 \leq a_2 \leq \cdots\}\) of integers such that 1. \(A\) remains complete after removing any \(m\) elements, but 2. \(A\) is not complete after removing any \(n\) elements. Geneson [Ge26, Theorem 1] proved that the pairs are exactly those with \(m \leq 1\). Completeness allows finitely many exceptions, and deletions remove indexed occurrences.