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Search: id:A003005
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| A003005 |
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Size of the largest subset of the numbers [1...n] which doesn't contain a 6-term arithmetic progression.
(Formerly M0459)
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+0
5
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| 1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 22, 22, 22, 23, 23, 23, 24, 25, 25, 26, 27, 28, 28, 29, 30, 31, 31, 31, 32, 33, 34, 34, 35, 36, 37
(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 6-free sequences.
The g.f. -(-1-z-z**2-z**3-z**4+z**5)/(z**4+z**3+z**2+z+1)/(z-1)**2 conjectured by S. Plouffe in his 1992 dissertation is wrong.
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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, A003003, A003004, A065825.
Sequence in context: A091863 A163296 A123731 this_sequence A006163 A053757 A106744
Adjacent sequences: A003002 A003003 A003004 this_sequence A003006 A003007 A003008
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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