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A326032
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a(2^x + ... + 2^z) = w(x) + ... + w(z), where x...z are distinct nonnegative integers and w = A000120.
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1
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0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 3, 3, 4, 4, 4, 4, 5
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OFFSET
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0,7
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COMMENTS
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a(2*n+1)=a(2*n).
a(n)=1 if and only if n > 1 is in A283526. (End)
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LINKS
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EXAMPLE
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For example, a(6) = a(2^2 + 2^1) = w(2) + w(1) = 2.
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MAPLE
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Bwt:= proc(n) option remember; convert(convert(n, base, 2), `+`) end proc:
f:= proc(n) local L, i;
L:= convert(n, base, 2);
add(L[i]*Bwt(i-1), i=1..nops(L))
end proc:
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MATHEMATICA
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bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Total[Length/@bpe/@(bpe[n]-1)], {n, 0, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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