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A140080
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Fix e = 3; a(n) = minimal Hamming distance between the binary representation of n and the binary representation of any multiple ke (0 <= k <= n/e) which is a child of n.
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11
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0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| A number m is a child of n if the binary representation of n has a 1 in every position where the binary representation of m has a 1.
In other words, this tells us how closely (in Hamming weight) we can approximate n "from below" by a multiple of e.
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LINKS
| Nadia Heninger and N. J. A. Sloane, Table of n, a(n) for n = 0..5000
N. J. A. Sloane, Fortran program for this and related sequences
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EXAMPLE
| If n = 14 = 1110_2, take k=2, ke = 6 = 110_2, which is Hamming distance 1 from n. This is the best we can do, so a(14) = 1.
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PROG
| See link for Fortran program.
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CROSSREFS
| For e=2 and 4 through 9 see A000035 and A140081 through A140086.
Cf. A140137, A140138, A140200-A140206.
Sequence in context: A025886 A117355 A086966 * A065359 A087372 A036431
Adjacent sequences: A140077 A140078 A140079 * A140081 A140082 A140083
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KEYWORD
| nonn
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AUTHOR
| Nadia Heninger (nadiah(AT)cs.princeton.edu) and N. J. A. Sloane (njas(AT)research.att.com), Jun 03 2008
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