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Search: id:A006997
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| A006997 |
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Partitioning integers to avoid arithmetic progressions of length 3.
(Formerly M0185)
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+0
2
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| 0, 0, 1, 0, 0, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 2, 3, 3, 4, 3, 3, 4, 0, 0, 1, 0, 0, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 2, 3, 3, 4, 3, 3, 4, 1, 2, 2, 3, 3, 4, 3, 3, 4, 4, 5, 5, 4, 5, 5, 6, 6, 7
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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a(n) = 0 iff n in A005836.
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REFERENCES
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Gerver, Joseph; Propp, James; Simpson, Jamie; Greedily partitioning the natural numbers into sets free of arithmetic progressions. Proc. Amer. Math. Soc. 102 (1988), no. 3, 765-772.
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LINKS
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J. Shallit, k-regular Sequences
J. Shallit, Number theory and formal languages, in D. A. Hejhal, J. Friedman, M. C. Gutzwiller, and A. M. Odlyzko, eds., Emerging Applications of Number Theory, IMA Volumes in Mathematics and Its Applications, V. 109, Springer-Verlag, 1999, pp. 547-570.
A. M. Odlyzko and R. P. Stanley, Some curious sequences constructed with the greedy algorithm, 1978
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FORMULA
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a(3n+k) = [ (3a(n)+k)/2 ], 0 <= k <=2.
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CROSSREFS
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Sequence in context: A032337 A058190 A055736 this_sequence A050605 A060571 A131555
Adjacent sequences: A006994 A006995 A006996 this_sequence A006998 A006999 A007000
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Jim Propp (propp(AT)math.wisc.edu)
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