cp's OEIS Frontend

A359400 Sum of positions of zeros in the reversed binary expansion of n, where positions in a sequence are read starting with 1 from the left.

%I A359400 #47 Mar 23 2024 20:26:12
%S A359400 1,0,1,0,3,2,1,0,6,5,4,3,3,2,1,0,10,9,8,7,7,6,5,4,6,5,4,3,3,2,1,0,15,
%T A359400 14,13,12,12,11,10,9,11,10,9,8,8,7,6,5,10,9,8,7,7,6,5,4,6,5,4,3,3,2,1,
%U A359400 0,21,20,19,18,18,17,16,15,17,16,15,14,14,13
%N A359400 Sum of positions of zeros in the reversed binary expansion of n, where positions in a sequence are read starting with 1 from the left.
%F A359400 a(n) = binomial(A029837(n)+1, 2) - A029931(n), for n>0.
%e A359400 The reversed binary expansion of 100 is (0,0,1,0,0,1,1), with zeros at positions {1,2,4,5}, so a(100) = 12.
%t A359400 Table[Total[Join@@Position[Reverse[IntegerDigits[n,2]],0]],{n,0,100}]
%o A359400 (C)
%o A359400 long A359400(long n) {
%o A359400   long result = 0, counter = 1;
%o A359400   do {
%o A359400     if (n % 2 == 0)
%o A359400       result += counter;
%o A359400     counter++;
%o A359400     n /= 2;
%o A359400   } while (n > 0);
%o A359400   return result; } // _Frank Hollstein_, Jan 06 2023
%o A359400 (Python)
%o A359400 def a(n): return sum(i for i, bi in enumerate(bin(n)[:1:-1], 1) if bi=='0')
%o A359400 print([a(n) for n in range(78)]) # _Michael S. Branicky_, Jan 09 2023
%Y A359400 The number of zeros is A023416, partial sums A059015.
%Y A359400 Row sums of A368494.
%Y A359400 For positions of 1's we have A029931, non-reversed A230877.
%Y A359400 The non-reversed version is A359359.
%Y A359400 A003714 lists numbers with no successive binary indices.
%Y A359400 A030190 gives binary expansion, reverse A030308.
%Y A359400 A039004 lists the positions of zeros in A345927.
%Y A359400 Cf. A000120, A048793, A069010, A070939, A073642, A328594, A328595, A344618, A359402, A359495.
%K A359400 nonn,base
%O A359400 0,5
%A A359400 _Gus Wiseman_, Jan 05 2023