The idea for these has been around a few years. Claudio Meller's A160851 appears to be a (currently) somewhat misguided attempt at enumeration, while Rajesh Bhowmick's A203024, fleshed out by Charles Greathouse, provides a seemingly complete listing of sums, including 9449 6-digit terms. My 17338 6-digit results yield only 9443 distinct sums. Why six fewer?
Apparently 6-digit sums are the first that allow the sums to be twice one of the addends (i.e., a = b). In A023086 we see that there are twelve such. It turns out that six of these are the six that are not in my 17338 sums (because I did not allow a = b):
251748 = 2 * 125874
257148 = 2 * 128574
285174 = 2 * 142587
285714 = 2 * 142857
517482 = 2 * 258741
825174 = 2 * 412587
The other six are included because they each had an alternate solution:
517428 = 2 * 258714 = 241587 + 275841
571428 = 2 * 285714 = 142857 + 428571
571482 = 2 * 285741 = 158724 + 412758
825714 = 2 * 412857 = 241587 + 584127
851742 = 2 * 425871 = 127584 + 724158
857142 = 2 * 428571 = 142857 + 714285 = 275418 + 581724 = 285714 + 571428
Addendum: Éric and Gilles had created A331468 for their triples.
Addendum: Éric and Gilles had created A331468 for their triples.
Joli, Hans, merci !-)
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