Problems with A000028/A000379.

[T. D. Noe]

I strongly recommend against changing the name or values of A000028 or A000379. The existing descriptions are accurate and consistent with the existing values. The sequences are very old, and may well be referenced in the literature.

I disagree that A131180 is any more natural than A000028. If anything, A000028 is simpler, since it legislates only a(1) while A131180 legislates both a(1) and a(2). The argument seems pointless, however, since A131180 = A026416 and should be merged into that sequence, not A000028.

My recommendations:

- Change only the relevant comments on A000028/A000379 to indicate that they are not amazing, with pointers to A064175/A064176.

- Add comments to A064175/A064176 to indicate that they are amazing. Add references to Roberts's "Lure of the Integers." Add b-files.

- Drop the A131180 comment referencing the amazing property of A000028/A000379. Merge A131180 in A026146, delete it from the database and reuse it’s A-number.

- Add comment to A026416 that A026416 = A000028 with an initial 1.

- Search out and update any other OEIS references to A000028, A000379, or A131180.

> -----Original Message-----
> From: Max Alekseyev [mailto:maxale at gmail.com]
> Sent: Thursday, December 20, 2007 3:38 AM
> To: T. D. Noe
> Cc: David Wilson; Sequence Fans
> Subject: Re: Problems with A000028/A000379.
> 
> On Dec 19, 2007 11:06 PM, T. D. Noe <noe at sspectra.com> wrote:
> 
> > Although I do not have the Lambek/Moser paper, but I did read
> Roberts'
> > "Lure of the Integers", which discusses the results of the
> Lambek/Moser
> > paper.  Roberts says that splitting the integers based on the
> infinitary
> > Moebius function leads the two sequences with the "amazing" property.
> > Hence, the comments in A000028/A000379 should really be in
> A064175/A064176.
> 
> A while ago I suggested Neil to move 1 over to A000028 to make its
> definition more natural. And the "amazing property" was the major
> reason to keep A000028/A000379 intact. Instead these new simplified
> variants were added as A131180/A131181.
> 
> If A000028/A000379 in reality do not possess the "amazing property",
> then I suggest to replace these sequences with A131180/A131181 and
> remove the latter pair.
> 
> Regards,
> Max