[seqfan] Re: Is the definition of this sequence correct?

Tom Duff eigenvectors at gmail.com
Sun Jul 3 21:01:25 CEST 2022

```I think this should read:
a(1)=1; a(n+1) is the smallest positive integer, distinct from all a(m),
m<=n, with |a(n+1)-a(n)|>=a(n).

Sequences, not their entries, are “lexicographically earliest”. The way a
sequence gets to be lexicographically earliest is by picking the smallest
eligible entry at each step. “Distance … in both directions” is best
expressed by explicitly saying that it’s the absolute difference.
All that said, I’m surprised that this sequence is not already in the OEIS.
Compute a bunch of terms (it’s easy, you shouldn’t need help) and search
for it. If it’s not there, add it.

On Sun, Jul 3, 2022 at 04:18 Ali Sada via SeqFan <seqfan at list.seqfan.eu>
wrote:

> Hi everyone,
>
>
> a(1) =1; a(n) is the lexicographically earliest positive integer such that
> the distance between a(n) and a(n)+1 is >= a(n) in both directions. (The
> distance between a(n) and a(m) is |n-m|)
>
> a(1) = 1
> a(2) = 2
> Now, a(3) cannot be 3, so a(3) = 4.
> a(4) cannot be 3 nor 5, so a(4) = 6.
> a(5) cannot be 3 nor 5 nor 7, so a(5) = 8.
> Now, we can use 3 for a(6) (the distance with 4 is 3).
> And so on.
>
> I would appreciate your help with the correct definition and terms.
>
> Best,
>
> Ali
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

```