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Search: id:A140081
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| A140081 |
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Period 4: repeat 0,1,1,2. |
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+0
3
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| 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Also fix e = 4; 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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FORMULA
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a(n)=(1/12)*{8*(n mod 4)-[(n+1) mod 4]+2*[(n+2) mod 4]-[(n+3) mod 4]}, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 06 2008
a(n)=1-(1/4)*(1-I)*I^n-(1/2)*(-1)^n-(1/4)*(1+I)*(-I)^n, with n>=0 and I=sqrt(-1) - Paolo P. Lava (ppl(AT)spl.at), Jul 17 2008
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PROGRAM
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See link in A140080 for Fortran program.
(PARI) a(n)=n%4-n%4\2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Aug 28 2009]
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CROSSREFS
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Sequence in context: A101660 A062984 A105243 this_sequence A112345 A124763 A029372
Adjacent sequences: A140078 A140079 A140080 this_sequence A140082 A140083 A140084
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KEYWORD
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nonn
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AUTHOR
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Nadia Heninger (nadiah(AT)cs.princeton.edu) and N. J. A. Sloane (njas(AT)research.att.com), Jun 03 2008
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