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A135136 a(n) = floor(S2(n)/2) mod 2, where S2(n) is the binary weight of n.

%I A135136 #15 Sep 28 2016 14:57:25
%S A135136 0,0,0,1,0,1,1,1,0,1,1,1,1,1,1,0,0,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,
%T A135136 1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,1,0,1,1,1,
%U A135136 1,1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0
%N A135136 a(n) = floor(S2(n)/2) mod 2, where S2(n) is the binary weight of n.
%C A135136 A generalized Thue Morse sequence.
%C A135136 A class of generalized Thue-Morse sequences: Let F(t) be an integer function, m,k integers. Let Sk(n) be sum of digits of n; n in base-k. Then a(n)= F(Sk(n)) mod m is a generalized Thue-Morse sequence. Thue-Morse sequence has F(t)=t (identity function), S2(n), m=2,k=2. Interesting properties have sequences where F(Sk(n))=floor(Q*Sk(n)); Q is a positive rational number; a(n)=floor(Q*Sk(n)) mod m. Another interesting sequences are a(n)=(n*Sk(n)) mod m; a(n)=(n+Sk(n)) mod m.
%D A135136 J. P. Allouche and J. Shallit, Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, 2003.
%H A135136 G. C. Greubel, <a href="/A135136/b135136.txt">Table of n, a(n) for n = 0..10000</a>
%H A135136 Ricardo Astudillo, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Astudillo/astudillo12.html">On a class of Thue-Morse type sequences</a>, Journal of Integer Sequences, Vol. 6 (2003), Article 03.4.2
%H A135136 R. Bacher and R. Chapman, <a href="http://dx.doi.org/10.1016/j.ejc.2003.06.001">Symmetric Pascal matrices modulo p</a>, European J. Combin. 25 (2004), 459-473.
%t A135136 Table[Mod[Floor[(Plus @@ IntegerDigits[n, 2])/2], 2], {n, 0, 90}] (* _Stefan Steinerberger_, Feb 14 2008 *)
%Y A135136 Cf. A010060.
%K A135136 nonn
%O A135136 0,1
%A A135136 _Ctibor O. Zizka_, Feb 13 2008
%E A135136 More terms from _Stefan Steinerberger_, Feb 14 2008