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Search: id:A072842
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| A072842 |
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Largest m such that we can partition the set {1,2,...,m} into n subsets with the property that we never have a+b=c for any distinct elements a, b, c in one subset. |
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+0
1
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OFFSET
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1,1
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COMMENT
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The fourth term is at least 66 (Ernst Munter), from { 24 26 27 28 29 30 31 32 33 36 37 38 39 41 42 44 45 46 47 48 49 } { 9 10 12 13 14 15 17 18 20 54 55 56 57 58 59 60 61 62 } { 1 2 4 8 11 16 22 25 40 43 53 66 } { 3 5 6 7 19 21 23 34 35 50 51 52 63 64 65 }
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REFERENCES
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EFNet #math, Jul 23 2002 (can we replace this with a link? - njas)
P. Bornsztein, An extension of a theorem of Schur, Acta Arithmetica, 101.4 (2001), pp. 395-399.
G. W. Walker, Solution to the problem E985, American Mathematical Monthly, Vol. 59 (1952), p. 253.
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LINKS
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Dr. Dobb's Journal, Solutions to the "Monopoles" Problem
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FORMULA
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It is known that 315^((n-1)/5) =< a(n) =< [n*e*(n!)] where [ ] denotes the integer part. - Pierre Bornsztein (bornsztein(AT)voila.fr), Sep 02 2003
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EXAMPLE
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a(2) = 8 because we may partition the set into {1, 2, 4, 8} and {3, 5, 6, 7} but in no other ways; attempting to add 9 to either will produce a set with the property that a+b=c for some a,b,c (1+8=9 or 2+7=9)
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CROSSREFS
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The requirement that a not equal b is the only difference between these numbers and the Schur numbers A045652.
Sequence in context: A014285 A079460 A018042 this_sequence A138387 A007346 A084744
Adjacent sequences: A072839 A072840 A072841 this_sequence A072843 A072844 A072845
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KEYWORD
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nonn,more,nice
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AUTHOR
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Tor G. J. Myklebust (pi(AT)flyingteapot.bnr.usu.edu), Jul 24 2002
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EXTENSIONS
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Additional comments from Rob Pratt and Brendan McKay, Nov 02 2002
More terms from Pierre Bornsztein (bornsztein(AT)voila.fr), Sep 02 2003
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