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arXiv · 1909.08849

The sum-of-digits function on arithmetic progressions

Lukas Spiegelhofer·Thomas Stoll
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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.

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Lukas Spiegelhofer, Thomas Stoll. 2019-09-19. The sum-of-digits function on arithmetic progressions. https://doi.org/10.2140/moscow.2020.9.43

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