The answer is yes, in fact the sequence $S\subset \mathbb{N}$ indexed by Thue-Morse sequence works, see this MO question. Note that this sequence is syndetic because it contains one of $\{2n, 2n+1\}$ for every $n$. You can extend to the negatives by reflecting and trivially only lose a factor of two on $\ell$.
Xiaoyu He
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