Abstract
In this note we use a sequence constructed by Furstenberg in 1981 to disprove the following conjecture posed by Brown: If a set of positive numbers L is such that for any finite coloring of N there are arbitrarily long monochromatic sequences of distinct integers with all gaps in L, then for any finite coloring of N there are arbitrarily long monochromatic arithmetic progressions whose common differences belong to L.
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