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A345972
Numbers that are integer multiples of the count of active segments in their 7-segment-display form where '6', '7' and '9' use 6, 3 and 6 segments, respectively.
1
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
OFFSET
1,2
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, ... see 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 numbers 4, 5 and 6 are the only entries that exactly equal their count of active segments.
REFERENCES
Heureka - Mathematische Rätsel 2021 - Tageskalender, Anaconda-Verlag, 2020, ISBN-978-3-7306-0881-4.
PROG
(Python)
def filter(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)
CROSSREFS
Sequence in context: A191208 A242077 A050162 * A224678 A049899 A217464
KEYWORD
nonn,base
AUTHOR
Marian Aldenhövel and Florentin Aldenhövel, Jun 30 2021
STATUS
approved