A366254 - OEIS

%I #17 Oct 06 2023 08:35:11

%S 0,1,2,1,2,1,2,3,4,1,2,3,2,3,2,3,4,1,2,3,2,3,2,3,4,5,2,3,4,3,4,3,4,1,

%T 2,3,2,3,2,3,4,5,2,3,4,3,4,3,4,5,2,3,4,3,4,3,4,5,6,3,4,5,4,5,6,1,2,3,

%U 2,3,2,3,4,5,2,3,4,3,4,3,4,5,2,3,4,3,4,3,4,5,6,3,4,5,4,5,4,5,2,3,4,3,4,3,4,5

%N Binary weight of May code (A303767).

%H Antti Karttunen, <a href="/A366254/b366254.txt">Table of n, a(n) for n = 0..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = A000120(A303767(n)).

%F a(n) = A001221(A303760(n)) = A001222(A303760(n)) = A001222(A366261(n)).

%F a(n) = A064547(A303771(n)).

%o (PARI)

%o A209229(n) = (n && !bitand(n,n-1));

%o A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644

%o A303767(n) = if(!n,n,if(A209229(n),n+A303767(n-1),A053644(n)+A303767(n-A053644(n)-1)));

%o A366254(n) = hammingweight(A303767(n));

%Y Cf. A000120, A001221, A001222, A064547, A303760, A303767, A303771, A366255, A366261.

%Y Cf. also A005811, A234022.

%K nonn

%O 0,3

%A _Antti Karttunen_, Oct 05 2023