Superexponentially decaying sequences in the Erdos similarity problem
We prove a non-universality criterion for the Erd\H{o}s similarity conjecture that applies beyond exponential (i.e., geometric) decay. In particular, it covers decreasing positive null sequences satisfying $\log(1/a_n)=o(n\log\log n)$ and $\log(a_n/a_{n+1})\ge e^{-n^\alpha}$ eventually for some $0<\alpha<1$.
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