Array of repeated conversions from decimal to base k

[N. J. A. Sloane]

JVP said:

The table begins as (row is what A-number):

1 | 10, 1111111111, ...
2 | 10, 1010, 1111110010, ... (A006937)
3 | 10, 101, 10202, 111222212, ... (A023372)
4 | 10, 22, 112, 1300, 110110, ... (A023378)
5 | 10, 20, 40, 130, 1010, 13020, ... (A023383)
6 | 10, 14, 22, 34, 54, 130, 334, 1314, ... (A023387)
7 | 10, 13, 16, 22, 31, 43, 61, 115, ... (A023390)
8 | 10, 12, 14, 16, 20, 24, 30, 36, 44, 54, ... (A008557)
9 | 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, ... (A023392)
10| 10, 10, 10, 10, 10, 10, 10, 10, ... (A010692)

Me: This is material that I will put into the index rather
than a new sequence.

Neil