OFFSET
0,6
COMMENTS
a(n) = Sum_{i=0..n} (-1)^(i+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 A020990, 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.
CROSSREFS
KEYWORD
sign
AUTHOR
Jeffrey Shallit, Feb 10 2023
STATUS
approved