[seqfan] Re: Inconsistency in A079749

[Pontus von Brömssen]

Thanks Hugo and Neil.

I started a draft for the corrected version: A358890.

I'm a bit skeptical about the convention gpf(1)=1, but I guess it's better
to keep it as close as possible to the original. (Without that convention,
a(3) would be 24 instead of 1.)

I have some more (minor) questions about how to handle this, see the pink
boxes for the new draft.

Cheers,

Pontus


On Mon, Dec 5, 2022 at 4:51 AM Neil Sloane <njasloane at gmail.com> wrote:

> hv:  Well said, I totally agree!
>
> Best regards
> Neil
>
> Neil J. A. Sloane, Chairman, OEIS Foundation.
> Also Visiting Scientist, Math. Dept., Rutgers University,
> Email: njasloane at gmail.com
>
>
>
> On Sun, Dec 4, 2022 at 10:25 PM <hv at crypt.org> wrote:
>
> > As far as I know, when we say "a run of exactly n" we mean one that
> > cannot be extended in either direction. So for the given definition,
> > the initial values of A079749 are wrong.
> >
> > That is certainly the interpretation that has been used in similar
> > sequences I have been involved with, such as A292580 where we have
> > T(6,8) = 18652995711772, T(6,9) = 15724736975643. For a different
> > interpretation we would necessarily have either T(6,8) = T(6,9),
> > or T(6,8) = T(6,9) + 1.
> >
> > Since all the relevant terms of A079749 have been there since 2003,
> > I think we need to create a new sequence with the correct terms, copy
> > over the other information, and then mark A079749 as an erroneous
> > version of the new sequence.
> >
> > I think sequences of "a run of at least n" are interesting in their
> > own right (and generally I prefer them to the "exactly" versions).
> > I don't think there's any sense in a run extensible in one direction
> > but not in the other - such a thing will always be a subrun of the
> > corresponding "run of at least n".
> >
> > Hugo
> >
> > =?UTF-8?Q?Pontus_von_Br=C3=B6mssen?= <pontus.von.bromssen at gmail.com>
> > wrote:
> > :Dear all,
> > :
> > :There is an inconsistency in the terms of A079749. The current
> definition
> > :is: "Consider the first occurrence of a run of exactly n successive
> > numbers
> > :whose greatest prime factors are monotonically increasing; a(n) is the
> > :first of these n numbers."
> > :
> > :The word "exactly" apparently means that the run cannot be extended, but
> > :does this include extensions in both directions? If it is sufficient
> that
> > :the run cannot be extended to the right, we would have the sequence 3,
> 2,
> > :1, 8, 90, 168, 9352, 46189, *721971*, 721970, 6449639, ...  (a(9)
> differs
> > :from the current data.) Alternatively, if it means that the run is
> > required
> > :to be maximal (not extendable in either direction), we would have the
> > :sequence *14*, *4*, 1, 8, 90, 168, 9352, 46189, 2515371, 721970,
> 6449639,
> > :... (a(1) and a(2) differ from the current data.)
> > :
> > :In both cases, I use gpf(n) =  A006530(n), which by convention equals 1
> > :when n = 1.
> > :
> > :I've written a comment about this in the sequence entry (and in a couple
> > of
> > :pink box comments). I'm aware that the preference is to change the
> > :definition if it's not consistent with the data, but in this case I
> cannot
> > :see how this could be done in a reasonable way, since different
> > definitions
> > :are used for different values of n.
> > :
> > :I would suggest changing the name to something like "a(n) is the first
> > term
> > :of the first maximal run of n consecutive numbers whose greatest prime
> > :factors are monotonically increasing." and change a(1) to 14 and a(2) to
> > 4.
> > :Any objections or other comments?
> > :
> > :Best regards,
> > :
> > :Pontus
> > :
> > :--
> > :Seqfan Mailing list - http://list.seqfan.eu/
> >
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> >
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