(In reply to

Puzzle Answer by K Sengupta)

Considering each members of the sequence as nase 3 integers and converting them to base 3, we have:

1,4,9,16,25,36

each of which is a perfect square.

The next two perfect squares are 49 and 64, which are respectably 1211 and 2101 in base 3.

Consequently, the required next two terms are 1211 and 2101.

*Edited on ***August 1, 2022, 10:30 pm**