Some properties of a Rudin-Shapiro-like sequence

Abstract

We introduce the sequence (in)n≥0 defined by in = (−1)inv2(n), where inv2(n) denotes the number of inversions (i.e., occurrences of 10 as a scattered subsequence) in the binary representation of n. We show that this sequence has many similarities to the classical Rudin–Shapiro sequence. In particular, if S(N) denotes the N-th partial sum of the sequence (in… (More)
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@article{Lafrance2014SomePO, title={Some properties of a Rudin-Shapiro-like sequence}, author={Philip Lafrance and Narad Rampersad and Randy Yee}, journal={CoRR}, year={2014}, volume={abs/1408.2277} }