A328109 Binary weight of A328103: a(n) = A000120(A110240(n) XOR A267357(n)).

0, 1, 4, 3, 5, 6, 8, 10, 9, 11, 11, 14, 14, 13, 16, 11, 18, 16, 17, 25, 18, 21, 25, 24, 22, 30, 25, 28, 30, 26, 33, 34, 36, 34, 33, 37, 37, 44, 38, 44, 51, 38, 43, 48, 45, 57, 38, 47, 50, 52, 49, 61, 53, 56, 63, 58, 56, 54, 60, 59, 64, 54, 60, 66, 69, 60, 67, 69, 72, 68, 75, 74, 77, 68, 78, 76, 75, 78, 72, 81, 80, 91, 78

Offset: 0

Author

Antti Karttunen, Oct 05 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A000120, A110240, A267357, A328103.

Cf. also A328105, A328106, A328107, A328108.

Programs

PARI

A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.
A110240(n) = if(!n,1,A269160(A110240(n-1)));
A269174(n) = bitand(bitor(n,n<<1),bitor(bitxor(n,n<<1),bitxor(n,n<<2)));
A267357(n) = if(!n,1,A269174(A267357(n-1)));
A328109(n) = hammingweight(bitxor(A110240(n),A267357(n)));
\\ Use this one for writing b-files:
A328109write(up_to) = { my(s1=1, s2=1); for(n=0,up_to, write("b328109.txt", n, " ", hammingweight(bitxor(s1, s2))); s1 = A269160(s1); s2 = A269174(s2)); };

Formula

a(n) = A000120(A328103(n)) = A000120(A110240(n) XOR A267357(n)).