[seqfan] Decimal concatenation of permutations

Charles Greathouse charles.greathouse at case.edu
Thu Apr 29 15:35:15 CEST 2010

I'm pretty sure that A079840 "Largest multiple of n as a concatenation
of its partitions", as written, is wrong.  It gives terms
1, 2, 21, 112, 5, 11112
and example
a(4) = 112: the partitions of 4 are 4,(3,1),(2,2),(1,1,2),(1,1,1,1).
There are two multiples of 4 i.e. 4 and 112. a(6) = 11112,(all
partitions with one even part give multiples of 6 and 11112 is the

The examples include one partitions listed in nonincreasing order
(3,1) and one in nondecreasing order (1,1,2).  I get different
sequences depending on what orderings I allow:
1,2,111,112,5,11112	nondecreasing only
1,2,111,4,5,222	nonincreasing only
1,2,111,112,5,11112	all orderings allowed

I can extend the sequence with any of these (though my code for the
last is atrocious), but I'm not sure which to use.

Charles Greathouse
Case Western Reserve University

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