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- W2056533610 abstract "We introduce the sequence $(i_n)_{n geq 0}$ defined by $i_n = (-1)^{inv_2(n)}$, where $inv_2(n)$ 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 $(i_n)_{n geq 0}$, we show that $S(N) = G(log_4 N)sqrt{N}$, where G is a certain function that oscillates periodically between $sqrt{3}/3$ and $sqrt{2}$." @default.
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- W2056533610 date "2014-08-10" @default.
- W2056533610 modified "2023-09-27" @default.
- W2056533610 title "Some properties of a Rudin-Shapiro-like sequence" @default.
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