[seqfan] 3,29,289,321,...

[Eric Angelini]

Hello SeqFans,
S= 3,29,289,321,3209,...

Look at 3 and 29:
we do 3*9 = 27
and 27+ 2 = 29

Look at 29 and 289:
we do 29*9 = 261
and 261 + 28 = 289

Look at 289 and 321:
we do 289*1 = 289
and 289 + 32 = 321

Look at 321  and 3209
we do 321*9 = 2889
and 2889 + 320 = 3209

...
The task is:
a(n)*[the last digit of a(n+1)]
+ [the string a(n+1) without the said digit]
= a(n+1)

Is this the start of the lexico-first such seq?
Best,
É.