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A359359
Sum of positions of zeros in the binary expansion of n, where positions are read starting with 1 from the left (big-endian).
24
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
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.
Sequence in context: A264357 A221573 A332453 * A240663 A066283 A267213
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Jan 03 2023
STATUS
approved