A365089 The Thue-Morse sequence along the sequence of cubes.

0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1

Offset

0

Comments

The set of n such that a(n)=0 has asymptotic density 1/2.

Links

Table of n, a(n) for n=0..99.

Lukas Spiegelhofer, Thue-Morse along the sequence of cubes, arXiv:2308.09498 [math.NT], 2023.

Formula

a(n) = A010060(n^3).

Mathematica

Table[ThueMorse[n^3], {n, 0, 100}] (* Amiram Eldar, Aug 21 2023 *)

Prog

(Sage) def a(n): return sum((n^3).digits(2))%2
(Python)
def A365089(n): return (n**3).bit_count()&1 # Chai Wah Wu, Aug 22 2023

Crossrefs

Cf. A010060, A000578, A228039.

Sequence in context: A219189 A029691 A209229 * A295890 A342704 A284622

Adjacent sequences: A365086 A365087 A365088 * A365090 A365091 A365092

Keyword

easy,nonn

Author

Lukas Spiegelhofer, Aug 21 2023

Status

approved