[seqfan] Re: Suggestion for a sequence

[Tom Duff]

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
>
>
>
>
> --
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