[seqfan] Re: Is the definition of this sequence correct?
Tom Duff
eigenvectors at gmail.com
Sun Jul 3 23:06:38 CEST 2022
No, sorry, my definition is bogus. The sequence is more complicated than I
made it out to be.
On Sun, Jul 3, 2022 at 15:01 Tom Duff <eigenvectors at gmail.com> wrote:
> 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,
>>
>> Please check this definition
>>
>> 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/
>>
>
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