[seqfan] Re: Close sequences

[Michael Porter]

I would definitely agree that a sequence that matches an existing sequence up to a(1000) and then diverges is a different sequence and deserves an independent entry.

However, that is not the case here.  As Maximilian has shown, this sequence is exactly the same definition as A003059 except for shifting one position and artificially setting the first term to zero.  I could see submitting the sequence if it were difficult to prove the sequences identical, or there was a sound mathematical reason for setting the first term to zero.

So I think you should hold off on submitting the sequence.

- Michael




--- On Sat, 10/17/09, Alonso Del Arte <alonso.delarte at gmail.com> wrote:

From: Alonso Del Arte <alonso.delarte at gmail.com>
Subject: [seqfan] Re: Close sequences
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Date: Saturday, October 17, 2009, 4:48 PM

That depends on how reasonable it is to expect that someone working
researching the topic in question would calculate one sequence but not the
other. If there's a good chance that that person would  input that sequence
into the OEIS and be surprised to a) not find it, or b) find several
seemingly unrelated results, then it ought to be added. But if the
researcher instead calculates the other sequence and is satisfied to find it
but not the other one, then maybe the first sequence isn't necessary in the
OEIS.
Also consider how likely your definition is likely to diverge from similar
sequences for some term too large to list in the OEIS. A long time ago I
remember Neil Sloane saying something to the effect that if two sequences
are the same up to a(1000) but after that gradually diverge more and more,
then both sequences ought to be in the OEIS even though they look the same
in the four lines that can be shown. But a comment noting the point of
divergence is worth adding. In your case, if you decide your sequence is
worth submitting, then your remarks on its similarities to A003059 ought to
be included as comments.

Al

On Sat, Oct 17, 2009 at 6:30 PM, Christopher Gribble <
chris.eveswell at virgin.net> wrote:

> Hello seqfans,
>
>
>
> I am considering submitting the following sequence:
>
>
>
> 0,2,2,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,
>
> 7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,
>
> 9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10
>
>
>
> For which the definition is:
>
>
>
> a(n) = minimum value of j, 1 <= j <= n-1, such that floor(j^2 / n) > 0 for
> each n.
>
>
>
> The sequence has been derived from the triangle of numbers presented in
> A166373.
>
>
>
> However, a(1) = 0 and a(2:) = A003059(3:).
>
>
>
> Should the sequence above have an independent existence in OEIS or not ?
>
>
>
> In general, how close can a new sequence be to a pre-existing sequence in
> OEIS to have its own entry ?
>
>
>
> Please advise.
>
>
>
> Best regards,
>
>
>
> Chris
>
>
>
> Christopher Hunt Gribble
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

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