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

Ali Sada pemd70 at yahoo.com
Mon Jul 4 00:26:22 CEST 2022

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Thank you, Tom. I really appreciate your response. It will take me some time to write a VBA program to find the terms. Manually, I will make mistakes!

Would any of these two versions work?

a(1)=1; a(n) is the least positive integer not already in the sequence such that the absolute distance between a(n) and a(n)+1 is >= a(n).

or

a(1)=1; a(n) is the least positive integer not already in the sequence such that |n-m1|>= a(n) and |n-m2|>= a(n)-1, where m1 and m2 are the indices of a(n)+1 and a(n)-1 respectively.

Best,

Ali

On Sunday, July 3, 2022 at 10:45:47 PM GMT+1, Tom Duff <eigenvectors at gmail.com> wrote:

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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