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

Author

N. J. A. Sloane, Jan 11 2011

Keywords

• nonn
• easy

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.

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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