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A281388 Write n in binary reflected Gray code and sum the positions where there is a '1' followed immediately to the right by a '0', counting the leftmost digit as position 1.

%I A281388 #15 Nov 22 2024 15:00:34
%S A281388 0,0,1,2,0,1,1,2,2,0,3,4,1,1,1,2,2,2,6,4,0,3,3,4,4,1,5,5,1,1,1,2,2,2,
%T A281388 7,7,2,6,6,4,4,0,5,8,3,3,3,4,4,4,9,6,1,5,5,5,5,1,6,6,1,1,1,2,2,2,8,8,
%U A281388 2,7,7,7,7,2,8,12,6,6,6,4,4,4,10,6,0,5,5,8,8,3,9,9,3,3,3
%N A281388 Write n in binary reflected Gray code and sum the positions where there is a '1' followed immediately to the right by a '0', counting the leftmost digit as position 1.
%H A281388 Indranil Ghosh, <a href="/A281388/b281388.txt">Table of n, a(n) for n = 1..10000</a>
%F A281388 a(n) = A049501(A003188(n)).
%e A281388 For n = 11, the binary reflected Gray code for 11 is '1110'. In '1110', the position of '1' followed immediately to the right by '0' counting from left is 3. So, a(11) = 3.
%e A281388 For n = 12, the binary reflected Gray code for 12 is '1010'. In '1010', the positions of '1' followed immediately to the right by '0' counting from left are 1 and 3. So, a(12) = 1 + 3 = 4.
%o A281388 (Python)
%o A281388 def g(n):
%o A281388     return bin(n^(n//2))[2:]
%o A281388 def a(n):
%o A281388     x=g(n)
%o A281388     s=0
%o A281388     for i in range(1, len(x)):
%o A281388         if x[i-1]=="1" and x[i]=="0":
%o A281388             s+=i
%o A281388     return s
%Y A281388 Cf. A003188, A014550, A049501.
%K A281388 nonn,base
%O A281388 1,4
%A A281388 _Indranil Ghosh_, Jan 21 2017