Concatenate a(n) and [sum of digits of a(n)]

[Eric Angelini]

Hello SeqFan,
I've started from the beginning and got:
 1-->11
 2-->22
 3-->33
...
 9-->99
10-->101
11-->112
12-->123
...
18-->189
19-->1910 (ouch!)
20-->202
21-->213
...

If I want to introduce in the OEIS the integers which
are at the right end of the arrow [-->] I will always
have the doubt that I've missed an integer somewhere
("202" in the above enumeration appears _after_ "1910",
though "202" will be in the sequence _before_ "1910")

Could someone help?

Second demand: are some numbers ambiguous? I mean, if
I give a such large number to someone explaining it's
hidden construction [concatenation of a(n) and sum of
digits of a(n)], might he find _another_ "primitive"
integer than me?

Best,
... and sorry if this is old hat...
E.