[seqfan] 2 Questions from a rank amateur newbie

Jerry zhivago47 at gmail.com
Wed Jun 2 00:56:19 CEST 2021

Hello. I note in the subject line that I am a rank amateur (in mathematics)
so that those who don't want to read the posts from such folks as I can
skip over the post without having to read any of it. I am a newbie with
reference to using the OEIS (and SeqFan).

1. My first set of questions is about submitting a new sequence to OEIS. I
submitted my first sequence about a week ago. After some very helpful
comments (thank you, Omar E. Pol, Andrew Howroyd, Michael S. Branicky), I
withdrew my submission because a better sequence, noted by Howroyd, already
existed. I now have another sequence I would like to submit, but given my
inexperience and lack of advanced math knowledge, I thought it might be
better to show it here for corrections and general feedback before
bothering folks on OEIS proper with it. If this is not a good idea, please
let me know.

The basic concept of this sequence is to give the percentage of 'integers
between square integers' that are primes. For example, between 9 and 16,
there are 6 integers, 2 of which are prime, so the 'percentage', in
fraction format, is 1/3. This sequence requires, as I understand it, the
submission of two sequences, one for the numerators and one for the
denominators, cross-referenced to each other. As I suspect is obvious, this
pair of sequences relates to Legendre's Conjecture (
https://en.wikipedia.org/wiki/Legendre%27s_conjecture )

I have searched OEIS for both these sequences (with 18 terms each) and
found no matches. However, I know from my brief experience that this same
information may already be in OEIS in some other format I haven't thought
of, and if so, not only is my proposed pair of sequences not needed, but
also the existing sequence is probably much better. So if anyone knows of a
form of this sequence already in the OEIS, please let me know, and it will
save a number of hard working editors and other folks at OEIS a bunch of

If such a sequence is not in OEIS, then I have several questions about the
format I should submit it in. Let me list the two sequences to start, just
for reference:
(numerators)  1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 2, 5, 5, 1, 1, 7, 5, 1, 3,
(denominators) 1, 2, 3, 8, 5, 3, 14, 4, 6, 4, 11, 24, 26, 7, 5, 32, 34, 6,

First question: The best name for these two sequences that I have been able
to come up with is:
(numerator/denominator of) fraction of integers, between n^2 and (n+1)^2
exclusive, that are primes, n>0.
>From other sequences I have looked at, my name doesn't seem very elegant.
Any improvements would be appreciated. Also, specifically, is the word
'exclusive' needed? Is 'n>0' needed (or does offset 1 take care of that)?
(I discuss the offset later in this post.)

Should 'references' be blank, because I know of no links that discuss this
particular fractional sequence? (If there were such a reference, then there
would probably already be a OEIS sequence for it, right?)

I could list a large number of 'links' about Legendre's Conjecture, and
most of them wouldn't say very much. Would it be sufficient to just list a
link like https://mathworld.wolfram.com/LegendresConjecture.html and let it
go at that?

Formula: I don't think (please correct me if I'm wrong) there is, properly
speaking, a formula for this sequence. Rather there is only an algorithm.
If so, should I put the algorithm in this section? If so, is the following
algorithm accurate? Is it the best algorithm?
Divided the primes between squares ( A014085, excluding first term) by the
gap between squares exclusive ( A005843, excluding the first term). Reduce
the resulting fraction.

Example: how many examples should I give, if any? Use something like n=3
and n=20?

See also: there are a number of sequences in OEIS related to Legendre's
Conjecture. Should I try to list all that I can find? Or should I list just
those that specifically relate to my algorithm (A014085 and A005843,
mentioned above)? Or something else or nothing?

keywords: The two keywords I believe are needed are frac and nnon. Correct?
Are there any others I should include?

offset: I believe this should be 1, correct? I notice, however,  that
A014085 and A005843 both use offset 0. For my sequence, n=0 is not
meaningless, since the denominator is not 0, but it  seems irrelevant to
me, but am I wrong? Should my sequence start with n=0?

If anyone has taken the trouble to read this far, thank you!

2. Second question: I mentioned at the beginning that I submitted a
sequence to OEIS and I withdrew it in under two days. I learned a lot from
the experience, and I was wondering if it would be worthwhile to post an
item with hints and recommendations for 'rank amateur newbies', like me. Of
course, it may be that newbies, especially those with limited math
knowledge, don't come to SeqFan. I looked and searched the topics in
SeqFan, and couldn't find any topic along the lines of help or hints--for
newbies or anyone else. Nor did I notice any topics that would 'prove' OEIS
newbies use SeqFan, although I easily may have missed topics that fit that

So, my question is, do you think such a post would have any value? If not,
might it be useful somewhere else? Of course, I would try to not duplicate
hints and recommendations that are easily found in OEIS itself. Probable
subjects would be: thinking of (and searching for) better sequences that
would do what your new sequence is meant to be used for; ways to search for
sequences in OEIS that are not mentioned in the OEIS instructions; where to
find different types of hints and explanations within OEIS.

Thank you to any and all who read this post, and especially to any who

Jerry Caveney

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