[seqfan] A126684

[Frank Adams-Watters]

Sequence https://oeis.org/A126684 has the statement that it is the 
fastest-growing sequence whose sumset is the non-negative integers. 
This is not obvious to me, and I don't see a proof or a link to a 
proof. It is easily shown that A126684(n) ~ n^2, and any sequence with 
this sum property must grow at least this fast. But that is not enough 
to say that it is the unique fastest growing. Note, btw, that this 
sequence does not grow as c n^2 + o(n^2); the ratio a(n)/n^2 is bounded 
but its lim inf is strictly less than its lim sup. This makes it a bit 
hard to tell exactly what "fastest-growing" actually means, here.

There are a number of links from  https://oeis.org/A000695, and I 
haven't checked them all to see if any support this claim. The deBruijn 
paper seems the most likely, but I can't tell from the front page, and 
it is behind a paywall.

Franklin T. Adams-Watters