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The sum-of-digits function on arithmetic progressions (1909.08849v1)
Published 19 Sep 2019 in math.NT
Abstract: Let $s_2$ be the sum-of-digits function in base $2$, which returns the number of non-zero binary digits of a nonnegative integer $n$. We study $s_2$ alon g arithmetic subsequences and show that --- up to a shift --- the set of $m$-tuples of integers that appear as an arithmetic subsequence of $s_2$ has full complexity.