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%I #26 Sep 17 2020 04:40:37
%S 0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,0,1,2,2,3,2,3,3,0,2,3,3,0,3,0,0,1,1,2,
%T 2,3,2,3,3,0,2,3,3,0,3,0,0,1,2,3,3,0,3,0,0,1,3,0,0,1,0,1,1,2,1,2,2,3,
%U 2,3,3,0,2,3,3,0,3,0,0,1,2,3,3,0,3,0,0,1,3,0,0,1,0,1,1,2,2,3,3,0,3
%N (Number of 1's in the binary expansion of n) mod 4.
%C This is the generalized Thue-Morse sequence t_4 (Allouche and Shallit, p. 335).
%D J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003.
%F a(n) = A010873(A000120(n)).
%t Nest[ Flatten[ # /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> {2, 3}, 3 -> {3, 0}}] &, {0}, 7] (* _Robert G. Wilson v_, May 17 2014 *)
%t Table[Mod[DigitCount[n,2,1],4],{n,0,110}] (* _Harvey P. Dale_, Jul 24 2016 *)
%o (PARI) a(n)=hammingweight(n)%4 \\ _Charles R Greathouse IV_, May 09 2016
%Y Cf. A000120, A010873, A010060 (mod 2), A071858 (mod 3).
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Jan 11 2011
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