[seqfan] Re: Suggestion for a sequence

[Tom Duff]

Bad on me, 0 is in the sequence. It's too hot out and too early in the
morning for me to be criticizing anything.

On Tue, Jun 29, 2021 at 11:36 AM Tom Duff <eigenvectors at gmail.com> wrote:
>
> It's a clever sequence solidly in the recreational math tradition. I
> think you should submit it.
> You have a small error: 0 shouldn't be in the sequence, it being the
> only non-negative number
> whose canonical decimal representation starts with a 0.
>
> On Tue, Jun 29, 2021 at 9:53 AM Marian Aldenhövel
> <marian.aldenhoevel at marian-aldenhoevel.de> wrote:
> >
> > Hi,
> >
> > I have a suggestion for a new entry into the OEIS. But as I hold the
> > Encyclopedia in very high regard and am purely an amateur I am a bit
> > intimidated by "The standards are those of a mathematics reference
> > work". So I would like to throw my possible contribution in here first
> > lest I do something really stupid.
> >
> > Maybe someone of the more seasoned people here can help me a bit. I am
> > looking for advice on both whether the sequence has any merit at all,
> > and if so help in making a proper submission.
> >
> > Find below what I have so far.
> >
> > Regards, Marian
> >
> >
> >
> > NAME
> >
> > Numbers that are integer multiples of the count of active segments in
> > their 7-segment-display form.
> >
> > DATA
> >
> > 0, 4, 5, 6, 16, 18, 21, 40, 45, 54, 60, 72, 81, 96, 110, 130, 132, 143,
> > 154, 156, 176, 180, 182, 195, 196, 224, 225, 238, 240, 255, 256, 273,
> > 306, 312, 320, 336, 341, 384, 400, 405, 408, 420, 442, 444, 450, 451,
> > 465, 481, 495, 496, 518, 525, 540, 555, 572, 592
> >
> > COMMENTS
> >
> > The sequence is given for 7-segment displays that format their digits
> > like so:
> >
> >   _     _   _        _   _   _   _   _
> > | | |  _|  _|  |_| |_  |_    | |_| |_|
> > |_| | |_   _|    |  _| |_|   | |_|  _|
> >
> > This sequence is infinite: For any n let e := sum_{i=0..n} 2*4^i (2, 10,
> > 42, ... A020988 <https://oeis.org/A020988>). The number a := 4*10^e is a
> > member of the sequence. It has 4+6*e active segments (one four and e
> > noughts).
> >
> > The number 4, 5 and 6 are the only entries that exactly equal their
> > count of active segments.
> >
> > REFERENCES
> >
> > "Heureka - Mathematische Rätsel 2021 - Tageskalender" Anaconda-Verlag
> > ISBN-978-3-7306-0881-4
> >
> > PROG
> >
> > (PYTHON)
> > def test(n):
> >      seg = 0
> >      for c in str(n):
> >          seg += { 0: 6, 1: 2, 2: 5, 3: 5, 4: 4, 5: 5, 6: 6, 7: 3, 8: 7,
> > 9: 6 }[int(c)]
> >      return(n % seg == 0)
> >
> > index = 0
> > n = 0
> > while (index < 10000):
> >      if test(n):
> >          index += 1
> >          print(f'{index} {n}')
> >      n += 1
> >
> > AUTHOR
> >
> > Marian Aldenhövel
> >
> >
> >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/