|
Search: id:A135136
|
|
|
| A135136 |
|
a(n) = floor(S2(n)/2) mod 2, where S2(n) is the binary weight of n. |
|
+0
3
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
A generalized Thue Morse sequence.
A class of generalised Thue-Morse sequences : Let F(t) be an integer function, m,k integers. Let Sk(n) is sum of digits of n; n in base-k. Then a(n)= F(Sk(n)) mod m is a generalised 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.
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 (stefan.steinerberger(AT)gmail.com), Feb 14 2008
|
|
CROSSREFS
|
Cf. A010060.
Adjacent sequences: A135133 A135134 A135135 this_sequence A135137 A135138 A135139
Sequence in context: A066247 A095792 A093385 this_sequence A137331 A093386 A011658
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Feb 13 2008
|
|
EXTENSIONS
|
More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 14 2008
|
|
|
Search completed in 7.381 seconds
|
