Let $D$ be an infinite (in one direction) sequence of zeros and ones. For each $n\in\mathbb{N}$, let $a_n$ denote the number of distinct subsequences of consecutive symbols in $D$ of length $n$. Does there exist a sequence $D$ for which the inequality \[ \left|\frac{a_n}{n\log_2 n} - 1\right| < \frac{1}{100} \]is satisfied for every natural number $n > 10^{10000}$?