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A006997
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Partitioning integers to avoid arithmetic progressions of length 3.
(Formerly M0185)
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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| a(n) = 0 iff n in A005836.
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| A. M. Odlyzko and R. P. Stanley, Some curious sequences constructed with the greedy algorithm, 1978
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.
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FORMULA
| a(3n+k) = [ (3a(n)+k)/2 ], 0 <= k <=2.
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CROSSREFS
| Sequence in context: A032337 A058190 A055736 * A141612 A050605 A060571
Adjacent sequences: A006994 A006995 A006996 * A006998 A006999 A007000
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jim Propp (propp(AT)math.wisc.edu)
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