|
Search: id:A064764
|
|
|
| A064764 |
|
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. |
|
+0
6
|
|
| 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)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
For n >= 4, a(n) >= A073818(pi(n)), with equality for 19 <= n <= 70. - David Wasserman (dwasserm(AT)earthlink.net), Aug 17 2002
|
|
REFERENCES
|
P. Erdos, R. Freud and N. Hegyvari, Arithmetical properties of permutations of integers, Acta Math. Hungar. 41 (1983), no. 1-2, 169-176.
|
|
LINKS
|
D. Wasserman, Proof of terms 11-70
|
|
FORMULA
|
a(n) = (1+o(1))n^2/(4 log n) as n -> infinity.
|
|
EXAMPLE
|
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.
|
|
CROSSREFS
|
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
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Oct 21 2001
|
|
EXTENSIONS
|
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 21 2001
Further terms from David Wasserman (dwasserm(AT)earthlink.net), Aug 17 2002
|
|
|
Search completed in 0.002 seconds
|
