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A272896 Difference between the number of odd and even digits in the decimal expansion of 2^n.

%I A272896 #19 May 22 2025 10:21:44
%S A272896 1,-1,-1,-1,0,0,-2,-1,-1,1,-2,-4,-2,0,-1,-1,1,2,-4,-4,-1,1,-1,-5,2,2,
%T A272896 -4,1,-3,1,0,-4,-2,2,3,3,1,4,-2,2,5,3,-1,-5,-2,-2,-2,1,-1,3,-4,0,2,2,
%U A272896 -1,-1,5,2,2,-4,-3,1,-5,-1,0,0,-6,3,5,5,2,-10,-8,2,-3,7,9,0,0
%N A272896 Difference between the number of odd and even digits in the decimal expansion of 2^n.
%C A272896 All vanishing entries are a(A272898(k)) = 0, k >= 1. - _Wolfdieter Lang_, May 24 2016
%H A272896 Indranil Ghosh, <a href="/A272896/b272896.txt">Table of n, a(n) for n = 0..10000</a>
%F A272896 a(n) = A055254(n) - A055253(n) = A196564(2^n) - A196563(2^n). - _Indranil Ghosh_, Mar 13 2017
%e A272896 2^10 = 1024, 2^11 = 2048, 2^12 = 4096, 2^13 = 8192.
%e A272896 So a(10) = 1 - 3 = -2, a(11) = 0 - 4 = -4, a(12) = 1 - 3 = -2, a(13) = 2 - 2 = 0.
%t A272896 Table[Count[#, _?OddQ] - Count[#, _?EvenQ] &@ IntegerDigits[2^n], {n, 0, 100}] (* _Michael De Vlieger_, May 09 2016 *)
%o A272896 (Ruby)
%o A272896 def a(n)
%o A272896   str = (2 ** n).to_s
%o A272896   str.size - str.split('').map(&:to_i).select{|i| i % 2 == 0}.size * 2
%o A272896 end
%o A272896 (0..n).each{|i| p a(i)}
%o A272896 (PARI) a(n) = #select(x -> x%2, digits(2^n)) - #select(x -> !(x%2), digits(2^n));
%o A272896 for(n=0, 78, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 13 2017
%o A272896 (Python)
%o A272896 def A272896(n):
%o A272896     x=y=0
%o A272896     for i in str(2**n):
%o A272896         if int(i)%2: x+=1
%o A272896         else: y+=1
%o A272896     return x - y # _Indranil Ghosh_, Mar 13 2017
%Y A272896 Cf. A000079, A055253, A055254, A196563, A196564, A272898.
%K A272896 sign,base
%O A272896 0,7
%A A272896 _Seiichi Manyama_, May 09 2016