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.

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

Author

Marian Aldenhövel and Florentin Aldenhövel, Jun 30 2021

Keywords

• nonn
• base

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.

Links

• Marian Aldenhövel, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to calculator display

Crossrefs

Cf. A006942, A020988.

Programs

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)