Zero-density conjecture for quotients of antipalindromic numbers

Let $Q_{\rm anti}$ be the set of integers representable as quotients of binary antipalindromic numbers. Zero-density conjecture. The set $Q_{\rm anti}$ has natural density zero.

The paper proves a lower bound of order $\sqrt{2}^{\,i}$ for the number of representable $i$-bit integers, but states that the zero-density assertion is difficult to prove.