[seqfan] Re: A126684

[Neil Sloane]

Did you try asking Jonathan Deane, the author of the sequence?
Neil

On Sat, Aug 30, 2014 at 4:42 PM, Frank Adams-Watters
<franktaw at netscape.net> wrote:
> 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
>
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Neil J. A. Sloane, President, OEIS Foundation
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