primes less than n and relatively prime to n--please folks!

[Marc LeBrun]

Is sombody which can indicated one or more sequences on ONEIS contributed  
by Marc LeBrun ?
ARTUR

Dnia 20-01-2007 o 01:16:31 Marc LeBrun <mlb at well.com> napisa³(a):

> Doesn't this seem like an awful lot of very random messages to a large  
> list in order resolve what seems to be a very small confusion?
>
> I apologize I don't have time to carefully thread through all the nearly  
> indecipherable postings trying to decode mysteries like what "A....."  
> refers to, "proofs" without a clear statement of any theorem, critiques  
> of documentation for programming languages, etc--so I might have missed  
> something.
>
> Nonetheless from just a cursory reading it seems clear--since SOME  
> primes less than n are NOT relatively prime to n (for example p=5,  
> n=100)--the qualifying clause in the subject line should be a perfectly  
> reasonable and necessary condition for a sequence.
>
> Don't you think that simply the number of times it appears in the OEIS  
> *might* indicate that it's saying something legitimate, whose meaning  
> might be extracted with just a little mental effort?
>
> So why are we making everybody read a zillion crazy postings about this?
>
> Maybe there needs to be a separate discussion group or something for  
> this kind of traffic?  Or else maybe we could exercise a bit more  
> restraint and/or engage in more 1-on-1 communications and/or simply  
> invest more thought before sending mail?
>
> I'm usually content to simply delete these kinds of messages, but I'm  
> beginning to see why that overhead might be driving people away.   
> Please, folks, let's do better.
>
> Thanks!
>
> (PS Apologies also if these suggestions have already been discussed to  
> death--I probably deleted those threads too!<;-)
>
>
>
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Thanks for asking!

I may fail here, but in the same constructive spirit let me try to 
help explain in a general way how you might evaluate such submissions 
yourself, *without* having to mail this list about each case like this.

This example IS highly artificial because there's no evident 
motivation for it *beyond* that it's vaguely like some other entry.

That "infinite number of such sequences" is a clear warning sign.

Indeed, why not go further and also include 2 [n/2] + 6 [n/3]?  Or 
[n/2] + [n/3] + [n/4]?  Can you give any specific non-arbitrary 
reason for excluding these?

Really it's analogous to asking why not include the values of EVERY 
polynomial; after all we are just replacing n^k with [n/k], right?

So, what does it take for the values of a polynomial to be 
interesting?  Once you can answer that you can generalize to other forms.

A simple heuristic is merely to consider whether the definition 
depends on arbitrary unmotivated choices.

For example simply replacing "integer" with "prime" or "Fibonacci" 
doesn't *by itself* create any additional new interest--unless there 
is some *other* good reason for it (for example primes because the 
has to do with phyllotaxis, or whatever).

bigger super class that contains your sequence or family, and then 
ask why your particular sub-case is more interesting on its own 
merits (independent of the predicate per se) than what you get by 
applying some other essentially arbitrary filter.

That is, does its essential character depend only on either arbitrary 
inclusions or exclusions?  If so, it's an artificial choice.

Another big warning sign is whether or not you would feel comfortable 
claiming there's any *reasonable* chance that the sequence will 
*ever* have anything to do with anything other than itself and 
closely similar variants.

As the many comments and references attest, A008615 relates to a 
whole bunch of disparate stuff besides its definition, so it passes muster.

But if you can't think of even one such interesting external 
connection, or at least imagine a way one might plausibly arise, then 
there's no known (non self referential) motivation, and there's a 
good chance you've merely just constructed something artificial.

Now that's not to say a *few* examples based on some elegant novel 
construction might not be OK *occasionally*--in moderation.  For 
example sum [n/k], k=1..m for m=1,2,3,4 maybe 5 or 6.  But starting 
at 2 and/or adding that restriction to prime k are both *INelegant* 
because there's no particular reason behind it motivating kludging in 
those extra conditions.

Really it's a kind of halting problem: One can always demonstrate 
unexpected or non-trivial connection with something else.  If you can 
establish such a connection, submit it.

Ask yourself, what would I put if the submission form actually 
*required* a "Why this is interesting" field?

But, for the contrary case--since it's impossible prove that 
weaker "effectively uninteresting" criteria for self-restraint.

So what you can do is try for a while to find something interesting 
about the item.  If you can't, after some time (how long is up to 
you), you conclude that you have not *established* that the sequence 
(at least until you can justify it).

It would be the same if it were just an encyclopedia of single 
numbers.  For example there's a few reasons I can cite for why 691 is 
interesting, but I can't offhand think of any good reason for 
"submitting" 690 or 692--simply being "like" 691 isn't enough.

Demonstrably interesting-->submit; not proven-->hold off until you can.

And of course you're generally expected to come up with your own 
justifications, rather than ask other people to try to find 
one--which is what querying the seqfans "Is this interesting?" really 
comes down to (have mercy, after all they have their own sequences to 
justify!<;-)

Hope this helps!


(By the way, A008615 is [n/2] - [n/3] not [n/4]).





Hello SeqFans,

A020735	Pisot sequence T(5,7). 	

and

A049013  Values of n such that a regular polygon with n sides can be formed by tying knots in a strip of paper.  	 	

are the same with different offset.

Does it mean that one of them should be dead?
Or they should reference each other?

Tanya