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%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