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Search: id:A050294
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| A050294 |
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Maximum cardinality of a 3-fold-free subset of {1, 2, ..., n}. |
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+0
3
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| 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 26, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 46, 47, 48, 49, 49, 50, 51, 51, 52, 53, 54, 55
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A set is 3-fold-free if it does not contain any subset of the form {x, 3x}.
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REFERENCES
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Bruce Reznick, Problem 1440, Mathematics Magazine, Vol. 67 (1994).
B. Reznick and R. Holzsager, r-fold free sets of positive integers, Math. Magazine 68 (1995) 71-72.
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LINKS
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S. R. Finch, Triple-Free Sets of Integers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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Take r = 3 in a(n) = (r n + sum [k = 0 to m] (-1)^k b(k)) / (r + 1), where [b(m) b(m-1) ... b(0)] is the base-r representation of n. - Rob Pratt (Rob.Pratt(AT)sas.com), Apr 21 2004
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CROSSREFS
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Cf. A050291-A050296.
Sequence in context: A103354 A127038 A051068 this_sequence A097950 A011885 A008672
Adjacent sequences: A050291 A050292 A050293 this_sequence A050295 A050296 A050297
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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More terms from John W. Layman (layman(AT)math.vt.edu), Oct 25 2002
Corrected and edited by S. R. Finch (Steven.Finch(AT)inria.fr), Feb 25 2009
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