4 is in the sequence since the sum of the first 4 lucky numbers, 1 + 3 + 7 + 9 = 20 is divisible by 4.
The corresponding last lucky number in each sum, the sum and the quotient are:
1 1 1 1 1
2 2 3 4 2
3 4 9 20 5
4 6 15 48 8
5 44 223 4488 102
6 124 777 44144 356
7 138 895 55890 405
8 224 1567 161280 720
9 620 5103 1466920 2366
10 4884 52291 120546888 24682
11 17482 213771 1777639688 101684
12 32130 416227 6378929550 198535
13 83185 1171177 46662209825 560945
14 253576 3902389 475856917960 1876585
15 276933 4289821 571527402075 2063775
16 386916 6145429 1145007096372 2959317
17 888823 14979331 6426527153917 7230379
18 12359950 245884005 1475626002615000 119387700
19 113944389 2555733867 141909851205948033 1245430797
20 129750250 2929396777 185255397118627500 1427784510
21 140503288 3184866705 218128021882008640 1552476280
22 143011869 3244610263 226192450002239721 1581634109
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