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

[Neil Sloane]

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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