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

Charles Greathouse charles.greathouse at case.edu
Thu Jun 24 15:22:13 CEST 2010

```I always consider 'how many of these are there' in like fashion.  I
came across a sequence recently that was defined as

(1) Primes of the form An^2 + Bn + C

for at least one of A, B, C large.  Now there are something like
A090025(k) possible sequences for 0 <= A,B,C <= k, and since in this
case there were negatives the number of possibilities was increased
almost eightfold.

Now I have no objection to sequences like (1), but if there are no
special properties to set it apart from the 1,814,311,873 other
sequences of the same form and <= its height, why are you including
it?

This has encouraged me to submit a signed version of A090025, though,
so not all is lost.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Wed, Jun 23, 2010 at 4:36 PM,  <franktaw at netscape.net> wrote:
> 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.
>
>
> -----Original Message-----
> From: Rick Shepherd <rlshepherd2 at gmail.com>
>
>
> 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
>>
>> 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: 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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