[seqfan] Re: Inconsistency in A079749

[hv at crypt.org]

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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