[seqfan] Re: A sequence and a few questions

[M. F. Hasler]

On Wed, Jul 5, 2023, 22:08 Ali Sada wrote:

> Hi
>
> 4.    If we tweak the definition a little bit: “Start with a list of
> positive integers 1,2,3,4… Take each number in the list (m) in turn and
> repeat it m times. Place the repeated numbers in non-consecutive locations
> such that the first appearance of m occurs at n = m.
>
> Gradually we will have 1,2,3,4,5,6,7…
> Is this sequence equal to A000027 (regardless of the fact that there are
> countless numbers that are supposed to appear “later”)?
>

Yes. The additional copies are all pushed away to infinity.
At the n-th step you set a(n) = n and from there on the subsequence
a(1...n) does not change any more; in subsequent steps you only modify
elements further away.
So in the limit the sequence has a(n) = n for all n ≥ 1, whence a =
oeis.org/A27

(PS: as a side note, what you call "countless" is (mathematically) still
 "countable"... ;-))

- Maximilian