cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A179868 #26 Sep 17 2020 04:40:37
%S A179868 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,
%T A179868 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,
%U A179868 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
%N A179868 (Number of 1's in the binary expansion of n) mod 4.
%C A179868 This is the generalized Thue-Morse sequence t_4 (Allouche and Shallit, p. 335).
%D A179868 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003.
%F A179868 a(n) = A010873(A000120(n)).
%t A179868 Nest[ Flatten[ # /. {0 -> {0, 1}, 1 -> {1, 2}, 2 -> {2, 3}, 3 -> {3, 0}}] &, {0}, 7] (* _Robert G. Wilson v_, May 17 2014 *)
%t A179868 Table[Mod[DigitCount[n,2,1],4],{n,0,110}] (* _Harvey P. Dale_, Jul 24 2016 *)
%o A179868 (PARI) a(n)=hammingweight(n)%4 \\ _Charles R Greathouse IV_, May 09 2016
%Y A179868 Cf. A000120, A010873, A010060 (mod 2), A071858 (mod 3).
%K A179868 nonn,easy
%O A179868 0,4
%A A179868 _N. J. A. Sloane_, Jan 11 2011