[seqfan] A modest chain

[Eric Angelini]

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.