[seqfan] Re: Bag of digits

[jnthn stdhr]

Will do.
On Dec 13, 2019 9:26 PM, "Neil Sloane" <njasloane at gmail.com> wrote:

> Jonathan:  very interesting construction!  certainly add those sequences to
> the OEIS!
>
>
> 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 Fri, Dec 13, 2019 at 1:11 PM jnthn stdhr <jstdhr at gmail.com> wrote:
>
> > Hi folks.
> >
> > Start with an empty bag of digits.  For each k =0,1,2,... compare the
> > digits of k with the contents of the bag.  If a digit of k matches a
> digit
> > in the bag throw them in the trash (they cancel each other out).  Add the
> > concatenation m of what remains of k to the sequence and toss the digits
> of
> > m into the bag.  Note that if m contains leading zeros they are stripped
> > away in the seq. but added to the bag.
> >
> > Initially no digits are in the bag so the first ten terms are
> > [0,1,2,3,4,5,6,7,8,9] and the bag contains (0,1,2,3,4,5,6,7,8,9).
> >
> > Now with k=10, we match both digits and nothing remains to add to the
> > sequence or the bag,so the sequence remains unchanged and the bag now
> > contains (2,3,4,5,6,7,8,9).
> >
> > With k=11, we match nothing, so 11 is added to the seq. ->
> > [0,1,2,3,4,5,6,7,8,9,11]  and two ones are added to the bag ->
> > (1,1,2,3,4,5,6,7,8,9).
> >
> > With k=12 and k=13, all digits are matched and the seq. is unchanged, and
> > the bag is left with (4,5,6,7,8,9)
> >
> > With k=14, the fours cancel and the one remains, so 1 is added to the
> seq.
> > and to the bag.
> >
> > Etc.
> >
> > The sequence begins:
> > [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 1, 1, 1, 20, 1, 22, 3, 4, 25, 6, 27,
> 8,
> > 29, 3, 33, 3, 3, 40, 1, 42, 3, 44, 5, 6, 47, 8, 49, 5, 5, 55, 5, 60, 1,
> 62,
> > 3, 64, 5, 66, 7, 8, 69, 7, 7, 7, 77, 80, 1, 82, 3, 84, 5, 86, 7, 88, 9,
> 9,
> > 9, 9, 9, 99, 100, 1, 2, 103, 4, 105, 6, 107, 8, 10, 1, 11, 11, 11, 11,
> 11,
> > 20, 1, 22, 13, 4, 125, 6, 127, 8, 129, 131, 33, 1, 13, 13, 140, 1, 42,
> 13,
> > 44, 15, 6, 147, 8, 149, 151, 5, 1, 55, 1, 15, 160, 1, 62, 13, 64, 15, 66,
> > 17, 8, 169, 171, 7, 1, 7, 1, 77, 1, 180, 1, 82, 13, 84, 15, 86, 17, 88,
> 19,
> > 191, 9, 1, 9, 1, 9, 1, 99, 200]
> >
> > The bag size always remains small.  For k > 9 record bag sizes occur at
> > (k:record size) 808:11, 8008:12, 10008:13, 80008:15, 800008:16,
> > 1000008:17.  Is there a simple explanation for why these k's all end with
> > an eight?
> >
> > The seq. of integers where no digits are canceled out is:
> > [0,1,2,3,4,5,6,7,8,9,11,20,22,25,27,29,33,40,42,44,47,49,55,60,...]
> >
> > The seq. of integers where all digits are canceled out is:
> > [10, 12, 13, 15, 17, 19, 30, 32, 34, 35, 37, 39, 50, 52, 54, 56, 57, 59,
> > 70, 72, 74, 76, 78, 79, 90, 92, 94, 96, 98, 112, 114, 116, 118, 130, 132,
> > 135, 137, 139, 150, 152, 157, 159, 170, 172, 179, 190, 192, 210, 213,
> 215,
> > 217, 219, 230, 235, 237, 239, 250, 257, 259, 270, 279, 290, 310,...]
> >
> > Should I add these?
> >
> > -Jonathan
> >
> > Python code:
> >
> > seq = []
> > bag = ""
> > #for first 10K term set range(11256)
> > for k in range(1000):
> >   m = str(k)
> >   for digit in m:
> >     if digit in bag:
> >       #Remove digit from m and bag.
> >       mndx = m.index(digit)
> >       m = m[:mndx] + m[mndx+1:]
> >       bndx = bag.index(digit)
> >       bag = bag[:bndx] + bag[bndx+1:]
> >   if m:
> >     seq.append(int(m))
> >     bag = bag + m
> >
> > print(seq)
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> --
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>