A079070 - OEIS

%I #18 Feb 15 2014 02:37:47

%S 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,

%T 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,

%U 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

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

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

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

%H Reinhard Zumkeller, <a href="/A079070/b079070.txt">Table of n, a(n) for n = 1..10000</a>

%e n = 12 -> '1100': A023416(12) = 2 therefore

%e a(12) = #{4 ->'100', 9 ->'1001', 10 ->'1010'} = 3;

%e n = 13 -> '1101': A023416(13) = 1 therefore

%e a(13) = #{2 ->'10', 5 ->'101', 6 ->'110', 11 ->'1011'} = 4.

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

%o (Haskell)

%o import Data.List (elemIndices)

%o a079070 n = length $ elemIndices (a023416 n) $ map a023416 [1..n-1]

%o -- _Reinhard Zumkeller_, Jun 16 20011

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

%K nonn,base,look

%O 1,6

%A _Reinhard Zumkeller_, Dec 21 2002