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We study a generalization of nonrepetitive sequences involving arithmetic progressions. We prove that for every $k\\geqslant 1$ and every $c\\geqslant 1$ there exist arbitrarily long sequences over at most $(1+\\frac{1}{c})k+18k^{c/c+1}$ symbols whose subsequences indexed by arithmetic progressions with common differences from the set $\\{1,2,...,k\\}$ are nonrepetitive. 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