A328105 Binary weight of A328104: a(n) = A000120(A110240(n) OR 2*A110240(n)).

2, 4, 5, 8, 7, 12, 9, 15, 11, 17, 17, 20, 19, 26, 21, 29, 22, 27, 30, 33, 30, 34, 37, 40, 37, 39, 41, 49, 44, 49, 48, 53, 41, 56, 49, 64, 50, 62, 59, 66, 64, 60, 66, 69, 61, 77, 65, 73, 67, 74, 70, 89, 78, 87, 78, 94, 85, 88, 89, 100, 91, 101, 95, 110, 92, 85, 98, 102, 102, 102, 115, 109, 101, 105, 121, 118, 121, 129

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, A163617, A269160, A328104.

Cf. also A070952, A328106, A328107, A328108, A328109.

Programs

PARI

A269160(n) = bitxor(n, bitor(2*n, 4*n));
A110240(n) = if(!n,1,A269160(A110240(n-1)));
A163617(n) = bitor(n,n<<1);
A328105(n) = hammingweight(A163617(A110240(n)));
\\ Use this one for writing b-files:
A328105write(up_to) = { my(s=1, n=0); for(n=0,up_to, write("b328105.txt", n, " ", hammingweight(bitor(s, s<<1))); s = A269160(s)); };

Formula

a(n) = A000120(A328104(n)) = A000120(A163617(A110240(n))).

For all n >= 0, A070952(a) < a(n) <= 2*A070952(n).