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A037879
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a(n) = (1/2)*Sum{|d(i)-e(i)|} where Sum{d(i)*2^i} is the base-2 representation of n and {e(i)} are digits {d(i)} in nondecreasing order.
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2
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0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1
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OFFSET
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1,19
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LINKS
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FORMULA
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a(2*n) = a(n). a(2*n+1) is either a(n) or a(n) + 1. - Robert Israel, Feb 08 2019
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MAPLE
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local a, dgs, dgsE ;
a := 0 ;
dgs := convert(n, base, 2);
dgsE := sort(dgs) ;
for i from 1 to nops(dgs) do
a := a+ abs(op(i, dgs)-op(i, dgsE)) ;
end do:
a/2 ;
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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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