mersenneforum.org General quibbles about some OEIS sequences
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 2021-12-13, 15:16 #1 Charles Kusniec     Aug 2020 Brasil 37 Posts General quibbles about some OEIS sequences Just to ask if you agree it is more intuitive also to define A100994(n) = A014963(n)^A325765(n) or A100994(n) = A014963(n)^A032741(n)?
 2021-12-14, 11:02 #2 Charles Kusniec     Aug 2020 Brasil 2516 Posts New sequence. If you also agree, I believe there is a missing sequence related to https://oeis.org/A100994. In the same way that we have https://oeis.org/A051451 without any repeated elements but document the https://oeis.org/A003418 with the proper repeated elements, for the sequence https://oeis.org/A181062 that has no repeated elements we have to document the indexes of the elements that do not generate records. Thus, we could create a new sequence related to https://oeis.org/A181062 as being $$AAAAAA = ( https://oeis.org/A100994 ) -1$$ whose first 60 elements would be {0, 1, 2, 3, 4, 0, 6, 7, 8, 0, 10, 0, 12, 0, 0, 15, 16, 0, 18, 0, 0, 0, 22, 0, 24, 0, 26, 0, 28, 0, 30, 31, 0, 0, 0, 0, 36, 0, 0, 0, 40, 0, 42, 0, 0, 0, 46, 0, 48, 0, 0, 0, 52, 0, 0, 0, 0, 0, 58, 0}. --- P.S.: the importance of recording the repeated elements (or at least their indices) is that they correctly reflect the repeated elements of the multiplication table (which is hyperbolic). Last fiddled with by Charles Kusniec on 2021-12-14 at 11:06
 2021-12-21, 11:29 #3 Charles Kusniec     Aug 2020 Brasil 37 Posts General questions about some OEIS sequences I will start with the sequence A056737. In my opinion, the complete and more general equation would be n = k*(k+-m). I would also take out the words "nonnegative" and "positive". To me, the following title would be more comprehensive: "Minimum integer m such that n = k*(k+-m) for integer k." or even just "Minimum m such that n = k*(k+-m)." I also think the example is half done. The complete one would be: a(8) = 2 because 8 = 2*(2+2) = 4*(4-2). This shows that every quadratic equation always has two roots. Do you agree?
 2021-12-21, 19:53 #4 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 11·19·47 Posts There is very little use posting your complaints about OEIS here. Only 1-2 people who are active there read this forum (I know a dozen editors there - that list has microscopic overlap with members of this forum). Solution: Step 1. Register at OEIS. Generally it is a Wikipedia-engine powered community. Easy to use if you had experience with Wikipedia. Step 2. Write your comments there - in each appropriate sequence.
 2021-12-21, 21:21 #5 rogue     "Mark" Apr 2003 Between here and the 19×347 Posts I find it annoying that there are multiple "flavors" of the same sequence, e.g. one sequence is a list of primes meeting certain criteria, another is a list of lengths of those primes, and another is the index of those primes. It pollutes OEIS because finding a new prime means that one has to update three sequences. I think that there would be value to changing OEIS to merge some of these, but I suspect that my opinion is in the minority.
2021-12-22, 10:18   #6
Charles Kusniec

Aug 2020
Brasil

37 Posts

Quote:
 Originally Posted by rogue I find it annoying that there are multiple "flavors" of the same sequence, e.g. one sequence is a list of primes meeting certain criteria, another is a list of lengths of those primes, and another is the index of those primes. It pollutes OEIS because finding a new prime means that one has to update three sequences. I think that there would be value to changing OEIS to merge some of these, but I suspect that my opinion is in the minority.
When it comes to polynomial sequences, I agree 100% that there are repeated sequences in the OEIS. In some cases, they do not make any sense. I will give only 2 examples, but there are many others:
search (17, 37, 59, 83, 109) you find A059425, A186950, A126665.
search (13, 29, 47, 67, 89, 113, 139, 167, 197, 229, 263, 299) you will find A243138 and A126719.
And so on...

This gives a feeling that there is no rigorous mathematical criterion in the treatment of polynomial sequences within the OEIS.

For me, there are 3 basic things that are missing:

1- The first thing is about positive and negative sign on the elements. Why we should have a duplicity of sequences just because of the exchange of signs between them? The search system should look for both positive and negative elements and if the sequence found has the sign changed, just adapt it. But certainly, the sign does not change the absolute values of the elements of any polynomial sequence.

2- The second thing is related to the direction of the sequence. Precisely when dealing with polynomial sequences, we cannot consider the existence of two different sequences just because of the direction of the elements. The sequence ...a,b,c,... is the same sequence as ...c,b,a... It only changes the way the reader reads it. This is why in any polynomial sequence we always have two recurrence equations. One towards the increasing indices and one towards the decreasing indices. In a way, this reflects the two edges of sequences of 1's in Pascal's triangle. Thus, the search engine must interpret the two sequences as one.

3- The third and last important thing about polynomial sequences is the offset. I see no reason why there should be repeated sequences in the OEIS just because we are looking at finite elements of an infinite sequence... Thinking about this I wrote the following articles in pre-print: https://easychair.org/publications/preprint/FQgX , https://easychair.org/publications/preprint/M18J ,
among others.

This lack of rigorous mathematical criteria in the presentations of polynomial sequence data results in facts such as the omission of the only negative number that exists in the sequence of numbers (squares minus 1). See that in the important sequence https://oeis.org/A005563 the important single element -1 is missing.

Another example occurs with the sequence http://oeis.org/A051872. The data do not show it, but the number 17 is the only prime number in this sequence. If we were to use the inflexion point (vertex) of polynomials as the offset reference parameter, we would put the sequence as ... 372 265 176 105 52 17 0 1 20 57 112 185 276 385 512 657 820 ...

At this point we clearly see that 17 is the only prime number of this sequence and we would also learn that it is an asymmetric sequence. This means that if one searches for the data (17, 52, 105, 176, 265, 372) we must find this same sequence http://oeis.org/A051872.

There are many other examples.

Finally, although I consider the OEIS to have these shortcomings, I also consider it to be a spectacular tool for working in mathematics. Additionally, it is not easy for an OEIS editor to evaluate the sequence proposals that appear. A small unnoticed detail results in an error. Sometimes it takes a long time for us to discover things that today are obvious.

2021-12-22, 14:27   #7
Charles Kusniec

Aug 2020
Brasil

37 Posts

Quote:
 Originally Posted by Batalov There is very little use posting your complaints about OEIS here. Only 1-2 people who are active there read this forum (I know a dozen editors there - that list has microscopic overlap with members of this forum). Solution: Step 1. Register at OEIS. Generally it is a Wikipedia-engine powered community. Easy to use if you had experience with Wikipedia. Step 2. Write your comments there - in each appropriate sequence.
Dear Serge (Batalov),

If you allow me, I understand that you will never find a complaint from me about the OEIS. On the contrary, I have a lot of respect and admiration for the work of the OEIS. I have never spoken ill of the OEIS.

However, some sequences and some patterns do not conform to the logical reasoning I have found in mathematics. I disagree with some sequences or decisions in the OEIS, but whenever I publish my disagreement I put the mathematical foundation to back it up. I have never disagreed on a whim.

Due to my disagreements, I have been expelled from the OEIS several times, but I have never taken it personally. I understand that the expulsions occurred because I failed to adequately explain the disagreement in that forum.

I have posted some disagreements here so that the members of this forum can give their mathematical opinions outside of the OEIS environment.

2021-12-22, 15:17   #8
Dr Sardonicus

Feb 2017
Nowhere

132158 Posts

Quote:
 Originally Posted by Charles Kusniec Dear Serge (Batalov), Due to my disagreements, I have been expelled from the OEIS several times, but I have never taken it personally. I understand that the expulsions occurred because I failed to adequately explain the disagreement in that forum. I have posted some disagreements here so that the members of this forum can give their mathematical opinions outside of the OEIS environment.
Let me see if I have this straight. The OEIS has found your complaints annoying or frivolous enough to have expelled you, more than once.

So now you're taking your complaints to this forum?

I suggest you pay attention.

2021-12-22, 18:03   #9
Charles Kusniec

Aug 2020
Brasil

1001012 Posts

Quote:
 Originally Posted by Dr Sardonicus Let me see if I have this straight. The OEIS has found your complaints annoying or frivolous enough to have expelled you, more than once. So now you're taking your complaints to this forum? Bad idea. Very bad. Reread this post. I suggest you pay attention.
Dear Dr. Sardonicus,

I am sorry to create an unnecessary polemic.

If it is possible, I would like to hear your technical opinion about the post https://www.mersenneforum.org/showpo...29&postcount=6.

Thank you very much.

2021-12-22, 18:37   #11
Charles Kusniec

Aug 2020
Brasil

37 Posts

Quote:
Dear VBCurtis,

The only reason I created this current thread is because it is the thought base for all (absolutely all) previous threads and explains the next ones I manage to post.

Thank you,

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