[seqfan] Re: A tricky sequence [A307720]

[Allan Wechsler]

This is a very interesting sequence. I have marked it as reviewed.

In A307720, do you need to specify that A(1) is 1? You could say, instead,
"lexicographically earliest sequence of positive integers" ... and then,
A(1) = 1 would follow from the conditions.

It also might be more perspicuous to say "... in which, for all positive k,
there are exactly k contiguous pairs whose product is k." The reference to
"a(n)" is confusing because you never actually use n.

With or without these changes: great idea!

On Wed, Apr 24, 2019 at 5:55 AM Éric Angelini <bk263401 at skynet.be> wrote:

> Hello SeqFans,
> a difficult challenge for your computer (and the quantity
> of memory it has):
>
> What is the smallest "n" here such that a(n) = 2019?
>
> The sequence exists only so far as a draft in the OEIS:
> https://oeis.org/draft/A307720
>
> It says:
> Lexicographically earliest sequence starting with a(1) = 1
> where a(n) is the number of pairs of contiguous terms whose
> product is a(n).
>
> DATA
> 1, 1, 2, 1, 3, 1, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3,
> 3, 3, 3, 3, 3, 3, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 4, 3, 4, 3,
> 4, 3, 4, 3, 4, 3, 5, 1, 5, 1, 5, 1, 7, 1, 7, 1, 7, 1, 7, 2,
> 5, 2, 5, 2,...
>
> A307720 will show all natural numbers sooner or later -- but,
> ahem, more "later" than "sooner"! So, what about 2019?
>
> The "twin" sequence was published yesterday (Belgium's time):
> https://oeis.org/A307707
>
> Best,
> É.
>
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>