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%I #29 Jan 01 2024 09:07:46
%S 0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,1,0,0,
%T 0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,0,0,
%U 0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,0,0
%N Take every third term of the {0,1}-version of the Thue-Morse sequence: a(n) = A010060(3n).
%C a(2n) = a(n). This is because the binary weight of 2(3n) is the same as the binary weight of 3n.
%C Characteristic sequence of A036556. Run lengths are A026497. - _Andrey Zabolotskiy_, Dec 31 2023
%H Antti Karttunen, <a href="/A293162/b293162.txt">Table of n, a(n) for n = 0..21846</a>
%H Alan Cobham, <a href="https://doi.org/10.1007/BF01706087">Uniform tag sequences</a>, Math. Systems Theory (1972) 6: 164-192. See Example 9.
%H Roswitha Hofer, <a href="https://doi.org/10.1016/j.disc.2011.04.008">Coquet-type formulas for the rarefied weighted Thue-Morse sequence</a> Discrete Mathematics 311.16 (2011): 1724-1734.
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F From _Antti Karttunen_, Dec 01 2017: (Start)
%F a(n) = A000120(3*n) mod 2.
%F a(n) = A010060(n) + A295890(n) mod 2. (End)
%F a(n) = A026492(n) - 1. - _Andrey Zabolotskiy_, Dec 31 2023
%t ThueMorse[Range[0,300,3]] (* _Paolo Xausa_, Dec 18 2023 *)
%o (Scheme) (define (A293162 n) (A000035 (A000120 (* 3 n)))) ;; _Antti Karttunen_, Dec 01 2017
%Y Cf. A000035, A000120, A010060, A005599, A026492, A026497, A036556, A293163, A293164, A295890.
%K nonn
%O 0
%A _N. J. A. Sloane_, Oct 15 2017
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