A360535 Analog of Rudin-Shapiro sum sequence A020986, based on counting patterns 00 instead of 11.

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

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

Table of n, a(n) for n=0..69.

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

Cf. A020985, A020990, A360536.

Sequence in context: A245343 A369858 A341019 * A255938 A081748 A322290

Adjacent sequences: A360532 A360533 A360534 * A360536 A360537 A360538

Keyword

nonn

Author

Jeffrey Shallit, Feb 10 2023

Status

approved