[seqfan] Re: SeqFan Digest, Vol 153, Issue 2

Jerry zhivago47 at gmail.com
Tue Jun 8 19:51:57 CEST 2021

Re: 2 Questions from a rank amateur newbie: thanks and follow up

Two preliminary notes: I apologize for the delayed response... I set myself
up on seqfan for what I thought was a daily digest, but it seems to have
created a weekly digest. After a few days of no digest, I switched to no
digest, but didn't receive my final digest until today, where my post and
the two responses were first visible to me, a week after I had posted.
Also, I'm not sure how best to respond to a digest. I simply did a reply to
the digest, and then deleted everything that I thought was not relevant to
my reply. If there's a better way to do it, please let me know.

So, first, thank you Hans and Sean! I appreciate the feedback. Hans, yes, I
do recognize that my proposed series is A014085/A005843. That is why I
mentioned those two sequences in my original post. It is also why I asked
if I should change my fractional sequence to offset 0, even though n=0
seems irrelevant to a sequence concerned with prime numbers. But it may
well be that since A014085 and A005843 have offset 0, it is more helpful to
make this new sequence offset 0 as well. I would appreciate feedback from
anyone on this point.

In response to you, Sean, yes, I read carefully the OEIS help files you
linked. My questions were on points that were still uncertain to me after I
had read them. Perhaps I should have understood more from the help files,
but I figured better to err on the side of safety.

As for my opinion on whether this proposed sequence has merit, I think it
does for the following reason: while it is true that A014085 covers the
same area as my sequence, it does not take into account the denominators of
my sequence. Thus it does not show, as n increases, how the frequency of
primes between squares decreases relative to the number of integers between
squares. For example, for n=5 (offset 0) the number of primes is 3, and the
fractional sequence is 3/8; but for n=20, the number of primes is 6, but
the fractional sequence is 3/19. So in this example, A014085 doubles from
n=5 to n=20, but the fractional sequence is more than halved. Thus it seems
to me that the fractional sequence provides very different information than
A014085 does.

I am acutely aware of my limited familiarity with OEIS and with my limited
knowledge of number theory compared with most everyone on this mail server.
So I would very much appreciate feedback on whether my proposed sequence
does indeed have merit to be included in OEIS or whether it would be a
waste of OEIS resources to include it. I will be happy to follow the
consensus opinion on this if there is one. Thank you to all who read this.


On Tue, Jun 8, 2021 at 9:07 AM <seqfan-request at list.seqfan.eu> wrote:

> ---------- Forwarded message ----------
> From: Jerry <zhivago47 at gmail.com>
> To: seqfan at seqfan.eu
> Cc:
> Bcc:
> Date: Tue, 1 Jun 2021 18:56:19 -0400
> Subject: [seqfan] 2 Questions from a rank amateur newbie
> 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
> trouble.
> 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,
> 19,
> 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
> criterion.
> 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
> respond.
> Jerry Caveney
> ---------- Forwarded message ----------
> From: Hans Havermann <gladhobo at bell.net>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Cc:
> Bcc:
> Date: Tue, 1 Jun 2021 19:27:12 -0400
> Subject: [seqfan] Re: 2 Questions from a rank amateur newbie
> "if anyone knows of a form of this sequence already in the OEIS"
> Excluding the zeroth terms this is A014085/A005843. Or is a division of
> two existing sequences not a "form" you would consider?
> ---------- Forwarded message ----------
> From: "Sean A. Irvine" <sairvin at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Cc: seqfan at seqfan.eu
> Bcc:
> Date: Wed, 2 Jun 2021 11:27:19 +1200
> Subject: [seqfan] Re: 2 Questions from a rank amateur newbie
> Your sequence is essentially already covered by A014085.  I don't see a lot
> of merit in repeating this sequence in fractional form as I think treating
> it as simple count is more natural than converting to a fraction (or worse
> percentage).
> With regard to your more general questions, it is perfectly fine for
> submissions to leave some fields (Formula, References, etc.) empty if no
> suitable information is available.
> The OeisWiki contains a wealth of information about making submissions and
> the meaning of the various fields.  Are you already familiar with that?
> e.g,
> https://oeis.org/wiki/Style_Sheet
> https://oeis.org/wiki/Overview_of_the_contribution_process
> Sean.

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