[seqfan] Re: Mystery of A049476

[jnthn stdhr]

In the paper, a gap is defined as where the algorithm first "breaks."   Not
the best choice of terms, IMHO.


On Monday, August 2, 2021, D. S. McNeil <dsm054 at gmail.com> wrote:

> Okay, combining the quote that Neil posted with reading the paper and
> comparing that with A049478 (the alleged size of the gap) made it clear
> what's going on.  In retrospect the quote should have sufficed but I have
> to admit it didn't until I read the relevant section of the paper. :-)
>
> The size of a gap is the minimum number g such that the leftmost elements
> of the row are the set {n,n-1...n-g} AND {n,n-1,...,n-g-1}, or
> equivalently, the row starts with the set {n,n-1,...,n-g} and the next
> element of the row is n-g-1.  If I understand the clear/break terminology
> of the paper, this is the first break.  (It's been a surprisingly long day,
> so I could have an offset wrong there in my description.)
>
> Using this criterion and taking the record locations and values of g, I
> get:
>
> (1, 0)
> (2, 1)
> (5, 4)
> (13, 6)
> (14, 12)
> (26, 22)
> (61, 27)
> (63, 62)
> (111, 64)
> (131, 84)
> (151, 104)
> (153, 106)
> (155, 108)
> (161, 114)
> (179, 132)
> (295, 142)
>
> where the first column is A049476 and the second is A049478.
>
> I would have had zero chance of figuring out that this is what was meant by
> "gap" without the additional information from Neil and the paper..
>
>
> Doug
>
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