[seqfan] Re: A126684
Frank Adams-Watters
franktaw at netscape.net
Sun Aug 31 02:15:53 CEST 2014
I have now.
njasloane at gmail.com
Franklin T. Adams-Watters
-----Original Message-----
From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Sat, Aug 30, 2014 6:00 pm
Subject: [seqfan] Re: A126684
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
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
--
Dear Friends, I have now retired from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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