[seqfan] Re: 4-12-28-60

[franktaw at netscape.net]

As the promulgator of the "rule of 2", I guess I ought to say something.

First, absolutely, any one clearly interesting fact about a sequence is 
sufficient reason to submit it. The rule of 2 applies when all you have 
are marginally interesting properties.

Let me give you an example of some sequences that I did not submit. 
Some time back, the question occurred to me as to whether there was a 
nontrivial multiplicative sequence that is also a permutation of the 
integers.

A bit of thought shows that there are many such sequences. A completely 
multiplicative permutation is obtained from any permutation of the 
primes. Also, a permutation can be readily obtained from any 
permutation of the numbers of the form p^2^n (A050376). But which 
permutation(s) to choose? One can just switch pairs of primes (2 3)(5 
7)(11 13)..., or take a single infinite cycle with 2 in the "middle", p 
== 1 (mod 4) on one side, and p == 3 (mod 4) on the other (... 13 5 2 3 
7 11 ...); or put 3 in the "middle", with p == 1 (mod 3) on one side 
and p == 2 (mod 3) on the other (... 17 11 5 2 3 7 13 19 ...), or .... 
For A050376, one can have a single cycle with primes on one side and 
higher powers on the other (... 25 16 9 4 2 3 5 7 ...); or swap p^2^2k 
with p^2^{2k+1}: (2 4)(3 9)(5 25)(7 49)(11 121)(13 169)(16 256)..., or 
.... And there are still other possibilities, e.g. based on p^3^k.

None of these really sticks out to me. So I'm left with submitting one 
or two dozen sequences, or none at all. By the rule of 2, if I can find 
some other, unrelated marginally interesting property possessed by one 
(or a few) of these sequences, I would submit it. There is one case 
where I did find such a property: A159253 (a(n) is the smallest 
positive integer not yet in the sequence such that n * a(n) is a 
cube.), which is the swap p^2^2k with p^2^{2k+1} described above  - 
though I would have submitted that sequence based on its defining 
property alone. Other than that, I haven't submitted any of these 
sequences. A few are already in the database: a quick search turns up 
A011262, A061898, A064614, A072026, A072027, A072028, A072029, and 
A108548.

Franklin T. Adams-Watters

-----Original Message-----
From: Rick Shepherd <rlshepherd2 at gmail.com>

Well said!  Please see my ("RS:") specific OEIS meta-comments below.

On Wed, Jun 23, 2010 at 2:00 PM, Marc LeBrun <mlb at well.com> wrote:

> >="K. Viswanathan Iyer" <kvi at nitt.edu>
> > Is the sequence defined by the D(n)'s interesting?
>
> Yes.  After verifying it's correct please submit it.
>
>
> It seems ironic that those folks who pause to worry about whether 
their
> submissions are sufficiently interesting almost certainly should 
contribute
> them, whereas those without a reflex for self-restraint cause the
> headaches.
>
> RS: Some of us sometimes even have to wait until late hours when the
self-restraint often diminishes as the "inner critic" (which/who usually
anticipates the other critics) begins dozing.  This shouldn't be 
necessary
but in the meantime I'm sure many of us have been sitting on large 
lists of
accumulating potential contributions.


> The OEIS is a cultural treasure chest.  But not everything in it can 
be a
> dazzling jewel, precious beyond measure.  Donating the product of any
> sincere investigation increases its value.  It just shouldn't be 
debased by
> flooding it with worthless plastic counterfeits.
>
RS: Very much agreed.


> RS: On the other hand, even when the definitions seem somewhat 
contrived
> (as opposed to intentional nonsense), they may have value at any time 
in
> helping say what another ostensibly-similar sequence is NOT.




> Further, it's a mine for new treasures, such as when superseeker etc
> reveals
> unexpected connections between sequences.  So submissions that might 
"salt"
> the OEIS for future findings might turn out to be more valuable than 
they
> at
> first appear.
>
> RS: This is where I agree wholeheartedly.  Although others may 
espouse a
"rule of 2" where some type of connections between two or more ideas or
sequences must be seen upfront even to warrant a submission (and I do
appreciate the value of that point of view), not all people are equally 
able
or motivated to find such connections -- and the original submission 
may be
just enough incentive for a second person (even years later) to draw -- 
and
report! -- the desirable connections. [Perhaps a better Rule of 2 -- if 
any
such rule is needed -- would be if at least *two people* see value in
something, but, then, again that would require a posting or discussion 
here
or somewhere.  Maybe it only makes sense to do so "before the fact" 
(i.e.,
before the actual work is done).]

RS: On a semi-related note, an encyclopedia that contains esoterica 
without
also having the most basic facts is suspect.  (In our defense, of 
course, we
are dealing (ironically) with uncountable facts so sometimes that's
unavoidable). [but see parts of Wikipedia (say, extensive pop culture 
topics
vs items of importance not there at all yet) to experience such 
undesirable
unevenness of coverage.]


> Generally (crank spew excepted) if it's interesting enough to you to 
expend
> the effort to research, compute, discuss and present in a 
well-crafted OEIS
> submission, then it is--ipso facto--interesting.
>
> RS: Again, FWIW, I agree. Thanks for your comments.

RS: One small example (years old?); I haven't checked lately to make 
sure
they're still not in the OEIS: Anyone want to find and add the two 
dihedral
angles of the buckyball in both degrees and radians (continued fractions
too)?  Feel free if you do.

Rick (Let's help keep Occam's Razor sharp.)

>
>
>
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