A179868 (Number of 1's in the binary expansion of n) mod 4.

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, 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, 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

Offset

0,4

Comments

This is the generalized Thue-Morse sequence t_4 (Allouche and Shallit, p. 335).

References

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003.

Links

Table of n, a(n) for n=0..100.

Formula

a(n) = A010873(A000120(n)).

Mathematica

Nest[ Flatten[ # /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> {2, 3}, 3 -> {3, 0}}] &, {0}, 7] (* Robert G. Wilson v, May 17 2014 *)
Table[Mod[DigitCount[n, 2, 1], 4], {n, 0, 110}] (* Harvey P. Dale, Jul 24 2016 *)

Prog

(PARI) a(n)=hammingweight(n)%4 \\ Charles R Greathouse IV, May 09 2016

Crossrefs

Cf. A000120, A010873, A010060 (mod 2), A071858 (mod 3).

Sequence in context: A376109 A354582 A359312 * A104232 A072086 A180094

Adjacent sequences: A179865 A179866 A179867 * A179869 A179870 A179871

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 11 2011

Status

approved