cp's OEIS Frontend

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

%I A079070 #28 Aug 03 2025 10:21:50
%S A079070 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 A079070 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 A079070 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 A079070 Number of numbers < n having in binary representation the same number of 0's as n.
%H A079070 Reinhard Zumkeller, <a href="/A079070/b079070.txt">Table of n, a(n) for n = 1..10000</a>
%F A079070 a(n) = #{m : m < n and A023416(m) = A023416(n)}.
%F A079070 a(2^k - 1) = k - 1; a(2^k) = 0; a(2^k + 1) = 1.
%e A079070 n = 12 -> '1100': A023416(12) = 2 therefore a(12) = #{4 ->'100', 9 ->'1001', 10 ->'1010'} = 3.
%e A079070 n = 13 -> '1101': A023416(13) = 1 therefore a(13) = #{2 ->'10', 5 ->'101', 6 ->'110', 11 ->'1011'} = 4.
%t A079070 dcn[n_]:=Count[Range[n-1],_?(DigitCount[#,2,0]==DigitCount[ n,2,0]&)]; Array[dcn,90] (* _Harvey P. Dale_, Jun 11 2011 *)
%o A079070 (Haskell)
%o A079070 import Data.List (elemIndices)
%o A079070 a079070 n = length $ elemIndices (a023416 n) $ map a023416 [1..n-1]
%o A079070 -- _Reinhard Zumkeller_, Jun 16 2011
%Y A079070 Cf. A068076, A079071, A079072, A007088, A023416.
%K A079070 nonn,base,look
%O A079070 1,6
%A A079070 _Reinhard Zumkeller_, Dec 21 2002