OFFSET
0,1
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.
MATHEMATICA
Table[Mod[Floor[(Plus @@ IntegerDigits[n, 2])/2], 2], {n, 0, 90}] (* Stefan Steinerberger, Feb 14 2008 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ctibor O. Zizka, Feb 13 2008
EXTENSIONS
More terms from Stefan Steinerberger, Feb 14 2008
STATUS
approved
