[seqfan] Inconsistency in A079749

[Pontus von Brömssen]

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