A grounded number sequence

There is no external source required, this relies only on maths.

Each line is independent from the others.
Can you find the pattern and fill in the blanks ?

1 : 0 0 0
2 : 1 2 3
3 : 4 2 9
4 : 1 2 3
5 : 7 7 9
6 : 4 0 6
7 : 2 4 9
8 : _ _ _
9 : 7 5 8
10: 5 9 5
11: _ _ _
12: _ _ _


Hint :

_A_B_C________________________________________________...

_ stands for 1 digit.

8:

9 8 9

11:

4 5 5

12:

3 0 5

The numbers are

the first three odd decimal digits of n^(1/n). For example, 2 gives us 1,414213...

• what the...? how did you end up looking in that direction? – Marius May 25 '16 at 11:56
• Well, it was a small step from "grounded" to "roots", the missing sequence for 8 8pointed me towards cubic roots initially, which worked with 3, but not the others... it was not too hard to connect the dots from there on. – cpj May 25 '16 at 12:00