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A360535 Analog of Rudin-Shapiro sum sequence A020986, based on counting patterns 00 instead of 11. 1
1, 2, 3, 4, 3, 4, 5, 6, 7, 6, 7, 8, 7, 8, 9, 10, 9, 10, 9, 8, 7, 8, 9, 10, 11, 10, 11, 12, 11, 12, 13, 14, 15, 14, 15, 16, 17, 16, 15, 14, 15, 14, 15, 16, 15, 16, 17, 18, 17, 18, 17, 16, 15, 16, 17, 18, 19, 18, 19, 20, 19, 20, 21, 22, 21, 22, 21, 20, 19, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) = Sum_{i=0..n} (-1)^e(i), where e(i) counts the (possibly overlapping) occurrences of 00 in the base-2 representation of n. Note that e(0) = 0. This is the analog of A020986, which is the same sum, but with e(n) replaced by the function that counts the (possibly overlapping) occurrences of 11 in the base-2 representation of n.
LINKS
N. Rampersad and J. Shallit, Rudin-Shapiro sums via automata theory and logic, Arxiv preprint arXiv:2302.00405 [math.NT], February 1 2023.
EXAMPLE
For n = 4, a(n) = 1+1+1+1+(-1) = 3.
CROSSREFS
Sequence in context: A245343 A369858 A341019 * A255938 A081748 A322290
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Feb 10 2023
STATUS
approved

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Last modified May 22 10:58 EDT 2024. Contains 372745 sequences. (Running on oeis4.)