A079070 Number of numbers < n having in binary representation the same number of 0's as n.

0, 0, 1, 0, 1, 2, 2, 0, 1, 2, 3, 3, 4, 5, 3, 0, 1, 2, 4, 3, 5, 6, 6, 4, 7, 8, 7, 9, 8, 9, 4, 0, 1, 2, 5, 3, 6, 7, 10, 4, 8, 9, 11, 10, 12, 13, 10, 5, 11, 12, 14, 13, 15, 16, 11, 14, 17, 18, 12, 19, 13, 14, 5, 0, 1, 2, 6, 3, 7, 8, 15, 4, 9, 10, 16, 11, 17, 18, 20, 5, 12, 13, 19, 14, 20, 21, 21, 15

Offset

1,6

Comments

a(n) = #{m : m < n and A023416(m) = A023416(n)};

a(2^k - 1) = k - 1; a(2^k) = 0; a(2^k + 1) = 1.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

n = 12 -> '1100': A023416(12) = 2 therefore
a(12) = #{4 ->'100', 9 ->'1001', 10 ->'1010'} = 3;
n = 13 -> '1101': A023416(13) = 1 therefore
a(13) = #{2 ->'10', 5 ->'101', 6 ->'110', 11 ->'1011'} = 4.

Mathematica

dcn[n_]:=Count[Range[n-1], _?(DigitCount[#, 2, 0]==DigitCount[ n, 2, 0]&)]; Array[dcn, 90] (* Harvey P. Dale, Jun 11 2011 *)

Prog

(Haskell)
import Data.List (elemIndices)
a079070 n = length $ elemIndices (a023416 n) $ map a023416 [1..n-1]
-- Reinhard Zumkeller, Jun 16 20011

Crossrefs

Cf. A068076, A079071, A079072, A007088, A023416.

Sequence in context: A330270 A029341 A240181 * A354787 A096994 A035370

Adjacent sequences: A079067 A079068 A079069 * A079071 A079072 A079073

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Dec 21 2002

Status

approved