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A037870
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a(n) = (1/2)*Sum{|d(i)-e(i)|}, where Sum{d(i)*2^i} is base 2 representation of n and e(i) are digits d(i) in nonincreasing order, for i=0,1,...,m.
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3
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0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2
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OFFSET
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1,12
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COMMENTS
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a(n) is also the minimum number of bit swap operations that needs to be performed to pack all the bits of n to the right. - Philippe Beaudoin, Aug 20 2014
The index of the k-th record of this sequence is A020522(k) and corresponds to k ones followed by k zeros. - Philippe Beaudoin, Aug 20 2014
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LINKS
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MAPLE
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a:= proc(n) local L, m;
L:= convert(n, base, 2);
m:= convert(L, `+`);
m - convert(L[1..m], `+`);
end proc:
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PROG
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(PARI) a(n) = {d = binary(n); e = vecsort(d); sum(i=1, #d, abs(d[i]-e[i]))/2; } \\ Michel Marcus, Aug 20 2014
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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