[seqfan] Re: Inconsistency in A079749

[Neil Sloane]

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
> :
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