[seqfan] A modest chain
Eric Angelini
Eric.Angelini at kntv.be
Wed Sep 17 12:54:23 CEST 2014
Hello SeqFans,
the beautiful "modest numbers" here https://oeis.org/A054986
gave me the idea of this "modest chain".
Start with 17 for instance:
17
Divide 17 by its highest digit and keep the remainder:
17/7 = (7*2)+3
Decide that the next term is the concatenation of 2 and 3 and iterate:
23/3 = (3*7)+2 --> 72
72/7 = (7*10)+2 --> 102
102/2 = (2*51)+0 --> 510
510/5 = (5*102)+0 --> 1020
1020/2 = (2*510)+0 --> 5100
5100/5 = (5*1020)+0 --> 10200
10200/2 = (2*5100)+0 --> 51000
etc.
We see that 17 enters into an "expanding loop".
Single-digit integers behave like that too:
8
8/8 = (8*1)+0 --> 10
10/1 = (1*10)+0 --> 100
100/1 = (1*100)+0 --> 1000 ...
Question:
Is 38 the smallest integer not entering into such a loop?
I have:
38,46,74,104,260,432,1080,1350,2700,3855,4817,6021,10033,33441,83601,104501,209001,232223,774072,1105815,...
Best,
É.
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