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

[neil greubel]

There is some form of explanation for the factorial base in the document of
( http://fs.unm.edu/Sequences-book.pdf  ) "Sequences of numbers involved in
unsolved problems" on page 32-33 and lists the double factorial base values
on page 33. Pages prior to page 32 have other examples.

In "Collected Paper vol 2"  ( http://fs.unm.edu/CP2.pdf ) pages 158-164
give some form of description of base numbers with page 164 giving the
values of the double factorial base.

On Sun, Mar 24, 2019 at 7:28 PM 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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