login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

The Thue-Morse sequence along the sequence of cubes.
1

%I #28 Aug 22 2023 14:14:45

%S 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,

%T 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,

%U 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

%N The Thue-Morse sequence along the sequence of cubes.

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

%H Lukas Spiegelhofer, <a href="https://arxiv.org/abs/2308.09498">Thue-Morse along the sequence of cubes</a>, arXiv:2308.09498 [math.NT], 2023.

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

%t Table[ThueMorse[n^3], {n, 0, 100}] (* _Amiram Eldar_, Aug 21 2023 *)

%o (Sage) def a(n): return sum((n^3).digits(2))%2

%o (Python)

%o def A365089(n): return (n**3).bit_count()&1 # _Chai Wah Wu_, Aug 22 2023

%Y Cf. A010060, A000578, A228039.

%K easy,nonn

%O 0

%A _Lukas Spiegelhofer_, Aug 21 2023