For any slowly growing function f, there exists a Poissonian pair correlation sequence whose number of distinct neighboring gap lengths is at most f(n), and for every such sequence the maximal gap multiplicity is o(n).
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On the number of gaps of sequences with Poissonian Pair Correlations
For any slowly growing function f, there exists a Poissonian pair correlation sequence whose number of distinct neighboring gap lengths is at most f(n), and for every such sequence the maximal gap multiplicity is o(n).