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A140085
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Period 8: repeat 0,1,1,2,1,2,2,3.
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1
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0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 1
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OFFSET
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0,4
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COMMENTS
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Also fix e = 8; then 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.
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.
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LINKS
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Table of n, a(n) for n=0..98.
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FORMULA
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a(n)=(1/56)*{24*(n mod 8)-4*[(n+1) mod 8]+3*[(n+2) mod 8]-4*[(n+3) mod 8]+10*[(n+4) mod 8]-4*[(n+5) mod 8]+3*[(n+6) mod 8]-4*[(n+7) mod 8]}, with n>=0 - Paolo P. Lava, Jun 06 2008
a(n) = 3/2 -cos(Pi*n/4)/4 -(1+sqrt(2))*sin(Pi*n/4)/4 -cos(Pi*n/2)/2 -sin(Pi*n/2)/2 -cos(3*Pi*n/4)/4 +(1-sqrt(2))*sin(3*Pi*n/4)/4 -(-1)^n/2. - R. J. Mathar, Oct 08 2011
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PROG
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See link in A140080 for Fortran program.
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CROSSREFS
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Sequence in context: A071227 A108115 A089254 * A071445 A144081 A140086
Adjacent sequences: A140082 A140083 A140084 * A140086 A140087 A140088
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KEYWORD
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nonn
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AUTHOR
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Nadia Heninger and N. J. A. Sloane, Jun 03 2008
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STATUS
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approved
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