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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.

%I A345972 #13 Jul 01 2021 04:30:44
%S A345972 0,4,5,6,16,18,21,40,45,54,60,72,81,96,110,130,132,143,154,156,176,
%T A345972 180,182,195,196,224,225,238,240,255,256,273,306,312,320,336,341,384,
%U A345972 400,405,408,420,442,444,450,451,465,481,495,496,518,525,540,555,572,592
%N 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.
%C A345972 The sequence is given for 7-segment displays that format their digits like so:
%C A345972    _     _   _        _   _   _   _   _
%C A345972   | | |  _|  _|  |_| |_  |_    | |_| |_|
%C A345972   |_| | |_   _|    |  _| |_|   | |_|  _|
%C A345972 .
%C A345972 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).
%C A345972 The numbers 4, 5 and 6 are the only entries that exactly equal their count of active segments.
%D A345972 Heureka - Mathematische Rätsel 2021 - Tageskalender, Anaconda-Verlag, 2020, ISBN-978-3-7306-0881-4.
%H A345972 Marian Aldenhövel, <a href="/A345972/b345972.txt">Table of n, a(n) for n = 1..10000</a>
%H A345972 <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>
%o A345972 (Python)
%o A345972 def filter(n):
%o A345972     seg = 0
%o A345972     for c in str(n):
%o A345972         seg += { 0: 6, 1: 2, 2: 5, 3: 5, 4: 4, 5: 5, 6: 6, 7: 3, 8: 7, 9: 6 }[int(c)]
%o A345972     return(n % seg == 0)
%Y A345972 Cf. A006942, A020988.
%K A345972 nonn,base
%O A345972 1,2
%A A345972 _Marian Aldenhövel_ and Florentin Aldenhövel, Jun 30 2021