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Search: id:A003003
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| A003003 |
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Size of the largest subset of the numbers [1...n] which doesn't contain a 4-term arithmetic progression.
(Formerly M0439)
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+0
6
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| 1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 17, 18, 18, 18, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 26, 26
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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These subsets have been called 4-free sequences.
Szemeredi's theorem for arithmetic progressions of length 4 asserts that a(n) is o(n) as n -> infinity. - Doron Zeilberger, Mar 26 2008
False g.f. (z**12+1-z**11-z**10+z**8-z**6+z**5-z**3+z)/((z+1)*(z-1)**2) was conjectured by S. Plouffe in his 1992 dissertation, but in fact is wrong (cf. A136746).
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. S. Wagstaff, Jr., On k-free sequences of integers, Math. Comp., 26 (1972), 767-771.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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CROSSREFS
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Cf. A003002, A003004, A003005, A065825.
Adjacent sequences: A003000 A003001 A003002 this_sequence A003004 A003005 A003006
Sequence in context: A067022 A113818 A136746 this_sequence A049474 A076874 A127041
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KEYWORD
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nonn,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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