OFFSET
1,1
COMMENTS
For n=19, the smallest integer from each triple does not belong to range [1,19]. Triplicating the sets of triples, shifting each triple to the left, generates permutations as in A070735, but not provably minimal ones.
a(n) >= ceiling(n*(3n!)^(1/n)) with the inequality tight for 1 <= n <= 3. - Chai Wah Wu, Mar 05 2020
LINKS
Martin Fuller, Table of n, a(n) for n = 1..80 (terms 1..50 from Rob Pratt)
Martin Fuller, Illustration of initial terms
Martin Fuller, Python program for this sequence
Chai Wah Wu, On rearrangement inequalities for multiple sequences, arXiv:2002.10514 [math.CO], 2020.
EXAMPLE
a(7)=4645 because (1*20*21)+(2*18*19)+(3*15*16)+(4*13*14)+(5*8*17)+(6*10*12)+(7*9*11)=4645 is the smallest value attainable.
PROG
(Python) See Martin Fuller link
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Wouter Meeussen, Jul 19 2002
EXTENSIONS
Corrected and extended via integer linear programming by Rob Pratt, Jul 28 2023
STATUS
approved