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%I #6 Dec 26 2021 10:39:01
%S 0,1,0,1,1,1,1,2,0,2,2,1,3,2,1,3,2,2,4,3,1,4,3,3,4,4,2,4,5,3,5,5,2,5,
%T 6,3,7,6,1,7,6,4,8,6,3,7,7,5,8,7,4,9,5,6,11,6,6,9,6,7,11,8,5,10,8,7,
%U 12,8,7,11,7,9,12,10,6,12,9,7,17,9,6,13,10,9,15,12,5,14,12,9,16,11,9,14,11
%N Number of ways n can be written as the sum of two numbers whose binary expansions have even numbers of zeros; also number of ways n can be written as the sum of two numbers whose binary expansions have odd numbers of zeros.
%C The only place where the two sequences differ is a(0) which is 1 for the odds and 0 for the evens.
%H IBM Ponder This, <a href="http://domino.watson.ibm.com/Comm/wwwr_ponder.nsf/challenges/February2001.html">Feb. 2001</a>
%H Y.-G. Chen and B. Wang, <a href="https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/110/3">On additive properties of two special sequences</a>, Acta Arith. 110 (3) (2003), 299-303.
%e a(16)=3 since 16=2+14=5+11=8+8 (in binary 10+1110=101+1011=1000+1000 where each term has an odd number of zeros) and since 16=1+15=4+12=7+9 (in binary 1+1111=100+1100=111+1001 where each term has an even number of zeros).
%Y Cf. A059009 and A059010 for the odd and even binary zeros sequences.
%K nonn
%O 1,8
%A _Henry Bottomley_, Feb 02 2001
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