A123756 a(0)=0. a(n) = number of earlier terms which are divisible by (the number of 1's in the binary representation of n).

0, 1, 2, 2, 4, 4, 5, 1, 8, 6, 7, 2, 8, 2, 2, 5, 16, 12, 13, 3, 13, 4, 4, 9, 15, 6, 7, 9, 8, 10, 10, 6, 32, 21, 21, 11, 21, 12, 13, 12, 23, 14, 14, 13, 14, 13, 13, 6, 27, 16, 16, 15, 17, 15, 15, 9, 20, 16, 17, 10, 17, 11, 11, 8, 64, 34, 35, 20, 36, 21, 22, 21, 38, 23, 23, 21, 24, 22, 22, 13

Offset

0,3

Links

Table of n, a(n) for n=0..79.

Example

9 in binary is 1001, which has 2 ones. So a(9) is the number of terms, from a(0) to a(8), which are divisible by 2. a(0)=0, a(2)=2, a(3)=2, a(4)=4, a(5)=4 and a(8)=8 are the six earlier terms which are divisible by 2. So a(9) = 6.

Mathematica

f[l_List] := Append[l, Count[Mod[l, Plus @@ IntegerDigits[Length[l], 2]], 0]]; Nest[f, {0}, 80] (* Ray Chandler, Oct 16 2006 *)

Crossrefs

Cf. A123755.

Sequence in context: A284432 A284435 A156130 * A357256 A300755 A307825

Adjacent sequences: A123753 A123754 A123755 * A123757 A123758 A123759

Keyword

easy,nonn

Author

Leroy Quet, Oct 12 2006

Extensions

Extended by Ray Chandler, Oct 16 2006

Status

approved