A359359 Sum of positions of zeros in the binary expansion of n, where positions are read starting with 1 from the left (big-endian).

1, 0, 2, 0, 5, 2, 3, 0, 9, 5, 6, 2, 7, 3, 4, 0, 14, 9, 10, 5, 11, 6, 7, 2, 12, 7, 8, 3, 9, 4, 5, 0, 20, 14, 15, 9, 16, 10, 11, 5, 17, 11, 12, 6, 13, 7, 8, 2, 18, 12, 13, 7, 14, 8, 9, 3, 15, 9, 10, 4, 11, 5, 6, 0, 27, 20, 21, 14, 22, 15, 16, 9, 23, 16, 17, 10

Offset

0,3

Links

Table of n, a(n) for n=0..75.

Formula

a(n>0) = binomial(A029837(n)+1,2) - A230877(n).

Example

The binary expansion of 100 is (1,1,0,0,1,0,0), with zeros at positions {3,4,6,7}, so a(100) = 20.

Mathematica

Table[Total[Join@@Position[IntegerDigits[n, 2], 0]], {n, 0, 100}]

Crossrefs

The number of zeros is A023416, partial sums A059015.

For positions of 1's we have A230877, reversed A029931.

The reversed version is A359400.

A003714 lists numbers with no successive binary indices.

A030190 gives binary expansion.

A039004 lists the positions of zeros in A345927.

Cf. A000120, A048793, A065359, A069010, A070939, A073642, A083652, A328594, A328595, A359402, A359495.

Sequence in context: A264357 A221573 A332453 * A066283 A240663 A267213

Adjacent sequences: A359356 A359357 A359358 * A359360 A359361 A359362

Keyword

nonn,base

Author

Gus Wiseman, Jan 03 2023

Status

approved