[seqfan] Re: A019513, numbers written in the base of double factorial numbers

[Neil Sloane]

Sean,  Thanks!

I made a couple of small edits to your A307102 and approved it.

Should you perhaps add a comment saying that this uses the greedy algorithm
to determine the coefficients?  (Because otherwise it is not unique.  And
not all weird-base expansions use the greedy rule - the Zeckendorf
expansion does not, for instance.)

I agree that Charles's comment is correct after all.  I misread the b-file
in A006882.  Well, I did it in a hurry, and I did ask you to check!

I will edit the original bad version right away.
Glad you caught the errors.

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 Sun, Mar 24, 2019 at 9:13 PM Sean A. Irvine <sairvin at gmail.com> wrote:

> Done, the new id is A307102.  Once approved I can add a b-file.
>
> I believe Charles' value is actually correct although your reasoning is
> correct as well -- you must have just miscalculated when looking for the
> first n!!, ten times larger than the previous.  It happens at 64!! not
> 49!!.
>
> Sean.
>
> On Mon, 25 Mar 2019 at 12:28, Neil Sloane <njasloane at gmail.com> wrote:
>
> > Sean,  I agree that there is something wrong.
> >
> > One has to use the greedy algorithm, unless there is some other
> > constraint, which does not seem to be the case here.
> > So certainly 30 should be 20000.  But since this is
> > such an old sequence, and may well be copied from some document of
> > Smarandache's (I didn't look at any of the references or links),
> > what I suggest is that you submit the correct version as a new sequence.
> > Then tell me the A-number,
> > and I will change the definition of A019513 to "Appears to be an
> erroneous
> > version of A...... "
> >
> > As to Charles Greathouse's comment,  it doesn't look right.  The question
> > is,
> > what is the first time we need a digit of 10 or more, so won't that
> happen
> > as soon as we get a double factorial that is more than ten times the
> > previous term?
> > So it would happen a 49!! times 10,
> > which is 584358414459472720534554743906250
> > Its representation would be 10 followed by 48 zeros - or something like
> > that.
> >
> > Can you check? Charles's value is
> > 1122755752855713895623244049306709034778906250
> > which seems too big.
> >
> >
> > 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 Sun, Mar 24, 2019 at 5:19 PM Sean A. Irvine <sairvin at gmail.com>
> wrote:
> >
> > > I'm having trouble reproducing A019513 (numbers written in the base of
> > > double factorial numbers).
> > >
> > > The bases for each position are 1, 2, 3, 8, 15, etc.   The problem
> occurs
> > > at a(30) for which I get the representation 20000 whereas the sequence
> > > lists a(30)=11201.  Both of these do give 30, as 20000 = 2*15 and
> 11201 =
> > > 15 + 8 + 2*3 + 1.  So there must be some extra condition for which
> > > representation to choose.
> > >
> > > My first thought was it must be the "smaller" representation, but the
> > > sequence lists a(6)=200 rather than a(6)=111; and a(8)=1000 rather than
> > > a(8)=210.
> > >
> > > Ideas?
> > >
> > > Sean.
> > >
> > > --
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> > >
> >
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> >
>
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