[seqfan] Re: a^2 + b^3 = c^4

[Alexander P-sky]

The way to resolve ambiguity due to cases when some "c" have multiple pairs
of  {a,b} solutions - is to index the "c" sequence by sorted (by
ascendency) values of "c" (as that was already proposed ) AND to attach
to each  3  sequences  (only 3 sequences - no more is needed) additional
file with indexed (same way as the "c" sequnce) number of {a,b} solutions
 for each "c".

Alexander R. Povolotsky

On Tuesday, May 6, 2014, Alex M <timeroot.alex at gmail.com> wrote:

> But then we face the question of -- what if someone wanted to find just the
> values of a? We could sort by values of a, or values of b, or values of c;
> we could have duplicates, or not, for the sequence we're sorting by. This
> gives me 12 sequences. It quickly becomes unreasonable. :-/
>
> ~6 out of 5 statisticians say that the
> number of statistics that either make
> no sense or use ridiculous timescales
> at all has dropped over 164% in the
> last 5.62474396842 years.
>
>
> On Tue, May 6, 2014 at 3:16 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
> > You mean there would have to be 6 sequences? I agree.
> >
> > Charles Greathouse
> > Analyst/Programmer
> > Case Western Reserve University
> >
> >
> > On Tue, May 6, 2014 at 5:26 PM, Andrew N W Hone <A.N.W.Hone at kent.ac.uk
> > >wrote:
> >
> > > The problem is that the sequences will not make any sense without
> > repeated
> > > numbers in the c sequence.
> > >
> > > 72 appears twice in the cc sequence because (as far as I understand
> what
> > > has been computed) there are
> > > precisely two pairs of positive integers (a,b) such that a^2+b^3 = c^4.
> > As
> > > we continue increasing c,
> > > it is likely that a particular value will need to be repeated more than
> > > twice (arbitrarily many times?) - as
> > > many times as there are corresponding pairs of values of a and b.
> > >
> > > If the c values are not repeated, then the (a,b) values will soon be
> "out
> > > of sync" with the values of c:
> > > e.g. eventually it might happen that the 150th terms in the a/b
> sequences
> > > correspond to the 145th value of c,
> > > and so on, with the  gap getting increasingly wider.
> > >
> > > Andy
> > > ________________________________________
> > > From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Charles
> > > Greathouse [charles.greathouse at case.edu]
> > > Sent: 06 May 2014 16:13
> > > To: Sequence Fanatics Discussion list
> > > Subject: [seqfan] Re: a^2 + b^3 = c^4
> > >
> > > We may want to add those ancillary sequences and link them to the main
> > > sequence, sure.
> > >
> > > Charles Greathouse
> > > Analyst/Programmer
> > > Case Western Reserve University
> > >
> > >
> > > On Tue, May 6, 2014 at 10:02 AM, Lars Blomberg <lars.blomberg at visit.se
> > > >wrote:
> > >
> > > > As I understand it, one of the main uses of OEIS it to find a
> possible
> > > > sequence based on a few values that has been found in some
> > investigation.
> > > >
> > > > Say we have found 71,72,75 and look for it,  then we will not find
> the
> > > > proposed "cc" sequence.
> > > > We have no way of knowing that 72 should be entered twice.
> > > > Similarly looking for 108,126,128 will not find the "bb" sequence
> > because
> > > > the order is not the same.
> > > >
> > > > Would it not be better to let the "c" sequence have the c values in
> > order
> > > > without duplicates.
> > > > The values a,b,c for all the solutions (including duplicates) can be
> > > > supplied as a file.
> > > >
> > > > The same for b (and a if we can compute it).
> > > >
> > > > /Lars
> > > >
> > > > -----Ursprungligt meddelande----- From: Jean-François Alcover
> > > > Sent: Tuesday, May 06, 2014 3:10 PM
> > > >
> > > > To: Sequence Fanatics Discussion list
> > > > Subject: [seqfan] Re: a^2 + b^3 = c^4
> > > >
> > > > The 3 "co-ordinated" sequences might look like this:
> > > >
> > > > aa = {28, 27, 63, 1176, 648, 433, 1792, 2925, 3807, 4785, 4941, 1728,
> > > 4500,
> > > > 6083, 7452, 7203,...}
> > > >
> > > > bb = {8, 18, 36, 49, 108, 143, 128, 126, 108, 136, 135, 288, 225, 23,
> > > 216,
> > > > 343,...}
> > > > cc = {6, 9, 15, 35, 36, 42, 48, 57, 63, 71, 72, 72, 75, 78, 90,
> 98,...}
> > > >
> > > > jfa
> > > >
> > > > 2014-05-06 12:18 GMT+02:00 Andrew N W Hone <A.N.W.Hone at kent.ac.uk>:
> > > >
> > > >  I'm not sure how the c sequence works as an index on the other two,
> > > since
> > > >> for the same
> > > >> value of c there could be more than one pair (a,b) whic