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Search: id:A064764
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| A064764 |
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Largest integer m such that every permutation (p_1, ..., p_n) of (1, ..., n) satisfies lcm(p_i, p_{i+1}) >= m for some i, 1 <= i <= n-1. |
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+0
6
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| 1, 2, 3, 4, 6, 6, 12, 12, 12, 12, 18, 18, 24, 24, 24, 24, 35, 35, 44, 44, 44, 44, 55, 55, 55, 55, 55, 55, 68, 68, 85, 85, 85, 85, 85, 85, 102, 102, 102, 102, 119, 119, 145, 145, 145, 145, 174, 174, 174, 174, 174, 174, 203, 203, 203, 203, 203, 203, 232, 232, 261, 261, 261
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For n >= 4, a(n) >= A073818(pi(n)), with equality for 19 <= n <= 70. - David Wasserman (dwasserm(AT)earthlink.net), Aug 17 2002
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REFERENCES
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P. Erdos, R. Freud and N. Hegyvari, Arithmetical properties of permutations of integers, Acta Math. Hungar. 41 (1983), no. 1-2, 169-176.
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LINKS
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D. Wasserman, Proof of terms 11-70
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FORMULA
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a(n) = (1+o(1))n^2/(4 log n) as n -> infinity.
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EXAMPLE
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n=6: we must arrange the numbers 1..6 so that the max of the lcm of pairs of adjacent terms is minimized. The answer is 632415, with max lcm = 6, so a(6) = 6.
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CROSSREFS
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Cf. A035106, A064796-A064797, A000720, A073818.
Sequence in context: A064778 A028335 A007464 this_sequence A123131 A000793 A062163
Adjacent sequences: A064761 A064762 A064763 this_sequence A064765 A064766 A064767
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 21 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 21 2001
Further terms from David Wasserman (dwasserm(AT)earthlink.net), Aug 17 2002
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