[seqfan] A triangle with a small delay

[Éric Angelini]

Hello SeqFan,
This triangle was inspired by https://oeis.org/A125588
where at each step C is the difference B-A between the
two terms immediately above C:
A   B
  C

My hope, with this new triangle, was that its descending
[up\left] to [down\right] diagonal (10, 1, 112, 483,...)
would show the same succession of digits as the sequence
itself, BUT with the smallest possible "delay\gap" between
the n-th term of the diagonal and the n-th term of the 
sequence (delay in terms of digits).
The delay, here, is a single digit at each step (except 
for the starting integer, of course -- here "10"):

Diagonal:   10 1 112 483 2513 13169 ...
Horizontal: 10 11 124 832 5131 31699 ...

10   11     124     832       5131     31699   ...
   1    113     708      4299     26568
     112    595     3591     22269
        483    2996     18678
           2513    15682
               13169

Questions: could this 1-digit gap be kept for ever?
Is the above seq the lexico-first?
Best,
É.