[seqfan] Re: Another planetary sequence

Thu Sep 15 21:38:55 CEST 2016

Okay, I do accept the decision to reject this sequence. Just let me add
that sometimes it is difficult to predict (for me at least) whether a
sequence will be accepted or not. Most sequences are mathematical sequences
and I think that is good. But there are a number of non-mathematical
sequences that were still accepted. Don't get me wrong, I am not
complaining that a sequence of someone else was accepted and mine was not.
I just mean sometimes it is not obvious to me whether a sequence is or is
not appropriate. So I rather submit a sequence that gets rejected than not
submitting a sequence.

Joerg raises an interesting point: How does one create good OEIS sequences?
I do not know how other contributors work in that regard, but I would love
to hear more about that. I, for example, often create sequences that have a
relation to some already existing sequence that interests me, for example
Wieferich primes (A001220). Or sequences that have some relation to some
topic or object that I find interesting. I have a large text file on my
computer where I develop new sequence ideas. That file currently has more
than 100 entries and most of them are not yet ready to submit (and some
probably never will be). Most of them are really related to mathematical
problems, but sometimes something from some other area crosses my mind and
I make a new section in my text file for it. And then it sits there for a
while and gets expanded now and then and at some point I may feel that it
looks somehow "finished" and "okay". That it is "okay" or "interesting" may
often be subjective.

At that point I start a draft for it and then submit it. I am often quite
unsure whether a sequence will or will not be accepted. But my personal
rule of thumb is to submit a sequence rather than not submit, because I
think withholding a potentially useful addition to the OEIS because of not
knowing whether it is acceptable or not would be much more harmful than a
submission that is recycled.

As Charles pointed out above, we discussed the particular sequence in
question and the long thread above seemed to indicate there is interest in
such a planetary sequence, so it seemed logical to me to submit it.

Mhm, this has become a rather long message, so I will stop here. I hope
this gives others a bit of an insight into my motives behind that
particular submission.

Best regards
Felix

2016-09-15 19:55 GMT+02:00 Neil Sloane <njasloane at gmail.com>:

> I guess this is a dispute where I need to step in and resolve things.
>
> I agree with Joerg, this is not appropriate for the OEIS.  It is not like
> it has appeared on an IQ test, which is a legit. reason for including a
> sequence which would otherwise not be appropriate. It seems contrived and
> not well-defined (given that the definition of "planet" is a bit fuzzy).  I
> recycled it.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Thu, Sep 15, 2016 at 1:39 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
> > > For an example of "not interesting/contrived" seemingly pertinent to
> this
> > discussion:
> > may I ask what ( https://oeis.org/draft/A276707 ) is supposed to convey?
> > "Number of planet from the Sun that is orbited by the n-th most massive
> >  natural satellite.
> >  5, 6, 5, 5, 3, 5, 8, 7, 7, 6, 6, 7, 7, 6, 6"
> >
> > This is a sequence I discussed with Felix after this email chain caught
> my
> > interest. It's an attempt to do a moon sequence in the right way: no
> units,
> > no rounding, and stable over hundreds of millions or billions of years.
> How
> > would you do a sequence like this? What do you think of the other
> > astronomical sequences in the OEIS?
> > https://oeis.org/wiki/The_multi-faceted_reach_of_the_OEIS#Astronomy
> >
> > Charles Greathouse
> > Case Western Reserve University
> >
> > On Thu, Sep 15, 2016 at 1:14 PM, Joerg Arndt <arndt at jjj.de> wrote:
> >
> > > Donning my "grumpy old man" hat ...
> > >
> > >
> > > The OEIS is about INTEGER sequences, finite or infinite.
> > > One can turn real sequences into integer sequences using
> > > some funny hammer like floor() or round(), this usually
> > > results in something of little interest.
> > >
> > >
> > > But integer sequences should still have some merit
> > > (most often/importantly of mathematical nature).
> > >
> > > For an example of "not interesting/contrived" seemingly
> > > pertinent to this discussion:
> > > may I ask what ( https://oeis.org/draft/A276707 )
> > > is supposed to convey?
> > > "Number of planet from the Sun that is orbited by the n-th most massive
> > >  natural satellite.
> > >  5, 6, 5, 5, 3, 5, 8, 7, 7, 6, 6, 7, 7, 6, 6
> > > "
> > > This is just depressing.
> > > And a maintenance problem.
> > >
> > >
> > > It appears to me that good sequences come up when one works on
> > > something that does NOT have creating sequences for the OEIS in mind
> > > in the first place.
> > >
> > >
> > > Best regards,   jj
> > >
> > > * Alonso Del Arte <alonso.delarte at gmail.com> [Sep 15. 2016 18:05]:
> > > > There exist infinitely many sequences, both finite and infinite. The
> > > > problem is to decide which ones are useful and/or interesting enough
> to
> > > be
> > > > worth including in this reference work. And then you also have to
> think
> > > > about how people are going to look it up to find it.
> > > >
> > > > Try the following Wolfram Alpha query: radius of moons of planets of
> > > Solar
> > > > System.
> > > >
> > > > Today, it didn't quite understand that query, and instead gave me for
> > an
> > > > answer that the planets have an average radius of 15,111 miles, and
> > this
> > > > sequence of number of moons: 0, 0, 1, 2, 63 (known), 61 (known), 27
> > > > (known), 14 (known). If you put in a search for the first four terms,
> > the
> > > > ones without the disclaimer, you get a couple thousand results.
> > > >
> > > > Number of moons certainly looks like a more straightforward sequence
> > than
> > > > comparing a planet's radius to the radius of its largest moon. But
> even
> > > > with this one we have a bunch of asterisks. And could it actually be
> > the
> > > > case that one of these planets' largest moon is an unknown moon?
> Sounds
> > > > unlikely, but it's still enough to cast doubt on both of these
> > sequences.
> > > >
> > > > Al
> > > >
> > > > On Wed, Sep 14, 2016 at 4:50 AM, Paul Barry <pbarry at wit.ie> wrote:
> > > >
> > > > > Expand  sqrt(1/sqrt(1-12x)).
> > > > >
> > > > >
> > > > > Cheers,
> > > > >
> > > > > Paul Barry
> > > > >
> > > > > ________________________________
> > > > > From: SeqFan <seqfan-bounces at list.seqfan.eu> on behalf of Brad
> Klee
> > <
> > > > > bradklee at gmail.com>
> > > > > Sent: 13 September 2016 23:07:30
> > > > > To: Sequence Fanatics Discussion list
> > > > > Subject: [seqfan] Re: Another planetary sequence
> > > > >
> > > > > Hi Felix,
> > > > >
> > > > > Again, it's a good idea to compute sequences such as this for the
> > > purpose
> > > > > of data analysis, and maybe even for a laugh. This one makes Mars'
> > > moons
> > > > > Phobos and Deimos look pitiful, and another funny observation...
> > > Jupiter is
> > > > > #1 when it comes to moons. Ha!
> > > > >
> > > > > But think about the "data flood". We probably don't have the
> manpower
> > > to
> > > > > enter every data sequence into the OEIS; though, this would be a
> > great
> > > > > "freedom of information act".
> > > > >
> > > > > To go back to my original criticism, I think the OEIS is usually
> > > focused on
> > > > > infinite series rather than finite sequences.
> > > > >
> > > > > There are lots of great series out there, even related to planets.
> > > > >
> > > > > Consider the "Schwarzschild Solution" , as described in:
> > > > >
> > > > > https://en.wikipedia.org/wiki/Two-body_problem_in_general_
> relativity
> > .
> > > > >
> > > > > There is an effective potential, for which the radius of minimum
> > > energy can
> > > > > be found by solving a quadratic equation. Expanding the potential
> > > around
> > > > > that r_0 we have something like:
> > > > >
> > > > > V(r) = V(r_0) + k*r^2 + . . .
> > > > >
> > > > > then we can calculate the scaled zero-radius
> > > > >
> > > > > R = (2 * k * m)^(1/4) * r_0
> > > > >
> > > > > and substitute into
> > > > >
> > > > > 1 - L/R^2
> > > > >
> > > > > as in the previous email, the energy-zero-order precession angle (
> up
> > > to a
> > > > > factor of 2 pi). We have the exact form for this term, but it's
> > nothing
> > > > > pretty to look at. It's much too long to fit into one tiny column
> of
> > an
> > > > > article page. So then, let us expand in powers of x=(G m Sqrt[M (m
> +
> > > > > M)])/(c L):
> > > > >
> > > > > 3*x^2 + (45/2)*x^4 + (405/2)*x^6 + (15795/8)*x^8 + (161109/8)*x^10
> +
> > > ...
> > > > >
> > > > > To compare with standards, take the first term:
> > > > >
> > > > > 2 Pi* 3*G^2* m^2 *M *(m + M)/(c* L)^2
> > > > >
> > > > > as in the wikipedia article, under the usual assumption (M+m)~M.
> > > > >
> > > > > So, how about the numerator / denominator series?
> > > > >
> > > > > Numerator: 3, 45, 405, 15795, 161109, 3383289
> > > > > Denominator: 1, 2, 2, 8, 8, 16
> > > > >
> > > > > Denominators look somewhat boring, but numerators are interesting,
> > and
> > > > >
> > > > > Not in the OEIS!
> > > > >
> > > > > I'll see if I can put this in later when I have double checked
> > > everything.
> > > > >
> > > > > Best Regards,
> > > > >
> > > > > Brad
> > > > >
> > > > >
> > > > >
> > > > > On Tue, Sep 13, 2016 at 8:21 PM, Felix Fröhlich <
> > felix.froe at gmail.com>
> > > > > wrote:
> > > > >
> > > > > > Thanks for all the further replies. What about the following
> > > sequence.
> > > > > Its
> > > > > > terms are really integers.
> > > > > >
> > > > > > Rank of size of largest natural satellite of n-th planet from the
> > Sun
> > > > > among
> > > > > > size of all natural satellites of the planets, or 0 if the planet
> > > has no
> > > > > > natural satellites.
> > > > > >
> > > > > > Terms are 0, 0, 5, 67, 1, 2, 8, 7
> > > > > >
> > > > > > Of course this sequence may be a bit problematic as well. It is
> > > still a
> > > > > > time-dependent sequence, although it probably won't change
> > > frequently.
> > > > > Also
> > > > > > I don't know if that new sequence is that more interesting and
> it's
> > > of
> > > > > > course still finite and relatively short.
> > > > > >
> > > > > > Like others in this thread, I have also thought about other
> > possible
> > > > > > planetary sequences. What came to my mind was to make a sequence
> > > related
> > > > > to
> > > > > > orbital resonances (like the 1:2:4 resonance involving Io, Europa
> > and
> > > > > > Ganymede), although I am not sure at the moment what that
> sequence
> > > could
> > > > > be
> > > > > > exactly.
> > > > > >
> > > > > > Best regards
> > > > > > Felix
> > > > > >
> > > > > > 2016-09-12 4:58 GMT+02:00 Brad Klee <bradklee at gmail.com>:
> > > > > >
> > > > > > > Hi Felix,
> > > > > > >
> > > > > > > Yes, the planets are of great interest to everyone, glad you
> are
> > > > > > > thinking about it!
> > > > > > >
> > > > > > > This sequence is somewhat interesting, but one shortcomming for
> > > OEIS
> > > > > > > is that it doesn't go on forever, terminates at n=8.
> > > > > > >
> > > > > > > Around noon it's a good time to go outside and look up to the
> > sun.
> > > > > > > Unless it happens to be hidden, Mercury is somewhere in the
> sky,
> > > and
> > > > > > > then how can you help but to wonder exactly what is going on,
> > > > > > > physically? With the gravity wave signals coming out of LIGO,
> > > everyone
> > > > > > > now believes in Einstein's theory, and maybe they even talk
> about
> > > it
> > > > > > > positively in the beer halls. Time changes everything. But some
> > > things
> > > > > > > even time has difficulty changing. How many people can do the
> > > > > > > calculations? For example, perihelion precession? It seems, not
> > so
> > > > > > > many. Maybe we can use OEIS to help with all of that.
> > > > > > >
> > > > > > > We can start with something along the lines of:
> > > > > > >
> > > > > > > http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/
> > node115.html
> > > > > > >
> > > > > > > but it's still difficult even if you know squares of the
> > > y-intercepts
> > > > > > > of the Legendre polynomials. This presentation is confounding,
> at
> > > > > > > least to me. Luckily I did figure out another _Big Equation_
> that
> > > > > > > works just as well __on all planetary data__.
> > > > > > >
> > > > > > > If you read through the following and referenced articles
> > therein:
> > > > > > >
> > > > > > > http://oeis.org/search?q=pendulum+klee&language=
> > english&go=Search
> > > > > > >
> > > > > > > you should get a decent idea as to how to find the exact
> > solutions
> > > of
> > > > > > > 1-D oscillation problems in Classical Mechanics as expansions
> in
> > an
> > > > > > > energy parameter, which leads along one branch to the famous
> > > Jacobian
> > > > > > > Elliptic integrals.
> > > > > > >
> > > > > > > In a pseudo-potential formulation that Gauss and later
> > Fitzpatrick
> > > > > > > suggest for a first analysis of planetary perihelion
> precession,
> > > you
> > > > > > > can essentially reduce the two-dimensional orbital motion to
> one
> > > > > > > dimension ( by conservation of angular momentum ), and do more
> > > exact
> > > > > > > solving along similar lines. This time not for the period, but
> > for
> > > the
> > > > > > > precession rate.
> > > > > > >
> > > > > > > Using Mathematica to expedite multiplication and addition, I
> > wrote
> > > the
> > > > > > > following equation two days ago:
> > > > > > >
> > > > > > > 1-L/r^2
> > > > > > > +a*( (-3/2)*L/r^4 + (-3)*L*v[3]/r^3 + (-15/4)*L*v[3]^2/r^2 +
> > > > > > > (3/2)*L*v[4]/r^2 )
> > > > > > > + a^2 *((-15/8 )*L / r^6 + (-15/2)* L * v[3]/r^5 + (-315/16)*
> L*
> > > > > > > v[3]^2/r^4 + (-315/8)* L *v[3]^3/ r^3 + (-3465/64)* L * v[3]^4/
> > > r^2 +
> > > > > > > ( 45/8 ) * L *v[4]/r^4 + (105/4)* L *v[3] *v[4]/ r^3 +
> (945/16)*
> > > > > > > L*v[3]^2 *v[4]/ r^2 + (-105/16)* L *v[4]^2/r^2 +(- 15/4)* L
> > > *v[5]/r^3
> > > > > > > + (-105/8)* L *v[3]* v[5]/ r^2 + (15/8)* L *v[6]/r^2 )
> > > > > > > +a^3 *( ...) + ... higher order in a ...
> > > > > > >
> > > > > > > which describes perihelion precession in a general isotropic
> > > central
> > > > > > > potential in terms of potential expansion coefficients v[i],
> > > angular
> > > > > > > momentum "L", radius "r", and energy "a". As a check, for
> values
> > > of (
> > > > > > > v[i], r ) determined from coulomb potential the whole expansion
> > > goes
> > > > > > > to zero for any pair of (L,a). The coulomb solutions are Kepler
> > > > > > > Ellipses fixed in space, i.e. no precession.
> > > > > > >
> > > > > > > It may seem silly to have such a big equation that gets even
> > > bigger,
> > > > > > > but lets just look at the results. We have to use potential
> > theory
> > > to
> > > > > > > calculate values for
> > > > > > >
> > > > > > > {a,r,v[1],v[2],v[3],v[4],v[5], ... }
> > > > > > >
> > > > > > > by transforming the data at
> > > > > > >
> > > > > > > http://nssdc.gsfc.nasa.gov/planetary/factsheet/
> > > > > > >
> > > > > > > This is the only hard part, but doesn't take too long. Plugging
> > in
> > > the
> > > > > > > numbers for Mercury, and scaling to arcseconds per year, we
> get,
> > > term
> > > > > > > by term:
> > > > > > >
> > > > > > > {4.67068, 0.747725, 0.10366, 0.0149433, 0.0022804}
> > > > > > >
> > > > > > > with folded sum
> > > > > > >
> > > > > > > {4.67068, 5.41841, 5.52207, 5.53701, 5.53929}
> > > > > > >
> > > > > > > which converges to a value near the 5.5 reported by Fitzpatrick
> > in
> > > his
> > > > > > > table 2. For other planets the convergence is much faster, and
> > the
> > > > > > > second order equation here should do just fine. The
> > > pseudo-potential
> > > > > > > for Mercury is the most significantly different from quadratic
> > > > > > > harmonic, so higher terms are noticeable.
> > > > > > >
> > > > > > > The interesting part of this analysis is that energy parameter
> > "a"
> > > > > > > takes into account the time-changing radius of planetary
> orbits,
> > > > > > > whereas I cannot see any time-changing radius of the orbits in
> > > > > > > Fitzpatrick's equations! In our approach there is a
> contribution
> > > > > > > independent of "a", but notice that for Mercury values
> > > > > > >
> > > > > > > 4.67068 =/= 5.5 ( Fitzpatrick value )
> > > > > > >
> > > > > > > and
> > > > > > >
> > > > > > > 4.6708 =/= 5.32 ( https://en.wikipedia.org/wiki/
> > > > > > > Tests_of_general_relativity )
> > > > > > >
> > > > > > > so we need to include the part that depends on how high in the
> > > > > > > effective potential the system is to get nearer to the correct
> > > answer.
> > > > > > > How does Fitzpatrick get 5.5 with his method? Still wondering
> > about
> > > > > > > that, especially if his expansion does indeed ignore terms
> > > depending
> > > > > > > on the energy of the orbit. ( Maybe a closed form summation
> along
> > > "a"
> > > > > > > ? Even then, does his expansion have cross terms such as  L
> *v[3]
> > > > > > > *v[4]/ r^3 ? ).
> > > > > > >
> > > > > > > You may already notice that there is a fractional sequence of
> > > > > > > coefficients in the big precession equation. We can ( and will
> )
> > > put
> > > > > > > this into the OEIS, as an irregular triangular. Although there
> is
> > > an
> > > > > > > infinite number of v[i] variables, there is a natural grading
> in
> > > the
> > > > > > > ring generated by all possible products of the variables, which
> > can
> > > > > > > already be seen in the first few terms. If you have term
> > > > > > >
> > > > > > > v[i]^p_i * v[j]^p_j *..../r^p_r
> > > > > > >
> > > > > > > Then the exponents must satisfy
> > > > > > >
> > > > > > > ( i - 2 )*p_i + ( j - 2 )*p_j + ... p_r = 2(N+1)
> > > > > > >
> > > > > > > so every row is finite. We'll just need to do a Lexicographic
> > > ordering
> > > > > > > of the variables and exponents, and accept that the triangle
> will
> > > > > > > probably have lots of zeros. While we're on the subject:
> > > > > > >
> > > > > > > ** Does anyone know of a canonical form in OEIS for such a
> > > sequence?
> > > > > > > Or a sequence along similar lines? **
> > > > > > >
> > > > > > > Anyways it's a good place to leave off. This idea may yet be
> > > > > > > confusing, but will be much easier to understand once its been
> > > > > > > published through a few different venues including the OEIS.
> > > > > > >
> > > > > > > Thanks for writing, happy planet gazing!
> > > > > > >
> > > > > > >
> > > > > > > <~~~?~~~~~~
> > > > > > >
> > > > > > >               ?
> > > > > > > ~~~~~~~~?~~~~~~~~~~~>
> > > > > > >
> > > > > > >           ~~?~~~>
> > > > > > >
> > > > > > > Watch out for troublesome syzygies!
> > > > > > >
> > > > > > >                          ~?~>
> > > > > > >
> > > > > > >
> > > > > > > Best regards,
> > > > > > >
> > > > > > > Brad
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > > On Sep 11, 2016, at 11:49 AM, Felix Fröhlich <
> > > felix.froe at gmail.com>
> > > > > > > wrote:
> > > > > > > >
> > > > > > > > Dear sequence fans
> > > > > > > >
> > > > > > > > I thought about the following sequence:
> > > > > > > >
> > > > > > > > Ratio of radius of n-th planet (under the current
> > IAU-definition
> > > of
> > > > > > > planet)
> > > > > > > > from the Sun to mean radius of its largest natural satellite,
> > > rounded
> > > > > > to
> > > > > > > > the nearest integer, or 0 if the planet has no natural
> > satellite.
> > > > > > > >
> > > > > > > > a(1)-a(8) are 0, 0, 4, 308, 27, 23, 32, 18
> > > > > > > >
> > > > > > > > The true ratios are of course not integer values, but the
> terms
> > > give
> > > > > an
> > > > > > > > idea of how large the largest moons of the planets are
> compared
> > > to
> > > > > the
> > > > > > > > planets themselves (i.e. these values are still useful for
> > > > > comparison,
> > > > > > > even
> > > > > > > > when rounded to integers in my opinion). The closer the value
> > is
> > > to
> > > > > 1,
> > > > > > > the
> > > > > > > > larger the largest moon is relative to its planet. The value
> > for
> > > > > > Earth's
> > > > > > > > moon is relatively small, meaning the Moon is large relative
> to
> > > > > Earth.
> > > > > > > >
> > > > > > > > There are already a number of sequences related to the
> planets
> > > in the
> > > > > > > OEIS,
> > > > > > > > but I would like to hear the opinion of other contributors
> > and/or
> > > > > some
> > > > > > of
> > > > > > > > the editors before submitting this, mainly because I think
> the
> > > > > sequence
> > > > > > > > will likely be rejected.
> > > > > > > >
> > > > > > > > It is probably a "dumb" sequence, not really mathematically
> > > > > > significant,
> > > > > > > > but sometimes such sequences are still enjoyable.
> > > > > > > >
> > > > > > > > Best regards
> > > > > > > > Felix
> > > > > > > >
> > > > > > > > --
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> > > > > > >
> > > > > > > --
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> > > > > > >
> > > > > >
> > > > > > --
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> > > > > >
> > > > >
> > > > > --
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> > > > >
> > > > >
> > > > >
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