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Search: id:A117548
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| A117548 |
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Values of n for which there exist d(1),...,d(n), each in {0,1,2}, and an r in {1,2} such that Sum[d(i)d(i+k),i=1,n-k]=r (mod 3) for all k=0,...,n-1. (Such a sequence is called a very(3,r) sequence. See the link.). |
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2
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OFFSET
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1,2
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COMMENT
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Theorem. Let a be a very(3,r) sequence of length n, for r=1 or 2, and let z be a sequence of n-1 0's. Then az(2a) is a very(3,3-r) sequence of length 3n-1, where 2a denotes the sequence {2a(i) mod 3, i=1,...,n}.
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LINKS
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John W. Layman, On A Generalization of Very Odd Sequences
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EXAMPLE
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For the sequence d=112102 we get Sum[d(i)d(i+k),i=1,n-k]={11,5,5,5,2,2}= {2,2,2,2,2,2) (mod 3) for k=0,...,5, so 6 is a term of the sequence.
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CROSSREFS
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Cf. A053006, A117549-A117551.
Sequence in context: A103025 A134080 A111300 this_sequence A014489 A033959 A090946
Adjacent sequences: A117545 A117546 A117547 this_sequence A117549 A117550 A117551
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Mar 28 2006
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