[seqfan] Numbers n such that (n+n+1) divides the concatenation [n, n+1]

[Eric Angelini]

I think this seq (not in the OEIS) starts like this:

C = 1,4,16,49,166,...

We have:
1+2 divides 12          ->       12/3=4
4+5 divides 45          ->       45/9=5
16+17 divides 1617      ->    1617/33=49
49+50 divides 4950      ->    4950/99=50
166+167 divides 166167  -> 166167/333=499
...
Pattern?
Best,
É.