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

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, 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, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0

Offset: 0

Author

Ctibor O. Zizka, Feb 13 2008

Keywords

• nonn

Comments

A generalized Thue Morse sequence.

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.

References

• J. P. Allouche and J. Shallit, Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, 2003.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Ricardo Astudillo, On a class of Thue-Morse type sequences, Journal of Integer Sequences, Vol. 6 (2003), Article 03.4.2
• R. Bacher and R. Chapman, Symmetric Pascal matrices modulo p, European J. Combin. 25 (2004), 459-473.

Crossrefs

Cf. A010060.

Programs

Mathematica

Table[Mod[Floor[(Plus @@ IntegerDigits[n, 2])/2], 2], {n, 0, 90}] (* Stefan Steinerberger, Feb 14 2008 *)

Extensions

More terms from Stefan Steinerberger, Feb 14 2008