[seqfan] a(n) terms of S have digitsum a(n)

[Éric Angelini]

Hello SeqFans,
inspired by https://oeis.org/A136317
Lexicographically earliest seq S of distinct positive terms
such that a(n) terms of S have digitsum a(n).

S = 1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,21,22,23,24,
25,26,27,28,29,31,32,33,34,35,36,37,38,39,41,42,43,44,45,
46,47,48,49,51,...

What is happening with S is easy:
1 term with DS1: {1} (the other terms with DS1, like 10, 100,... are forbidden)
2 terms with DS2: {2, 11} (the other terms with DS2, like 20, 101,... are forbidden)
3 terms with DS3: {3, 12, 21} (no to 30, 102, 111, 120, 300,...)
4 terms with DS4: {4, 13, 22, 31} (no to 40, 103, 112, 121,...)
etc.
Best,
É.