[evil_twin]

Gumpzilla beat me to it, my solution matches his, although I had to write it out in detail to convince myself of it. Might as well post the solution for those wanting it spelt out (like me!) :

<font color="white">
It's a "look and say" sequence intertwined with some succesive prime number multiplication.

So, if we start at the beginning, we can explain all the terms:

1
We get the next term by multiplying by the first prime (2)
1x2 = 2

Next term from "look and say". The first term is "one one" so it's 11.
11
11x(the next prime) = 11x3 = 33

Next term from look and say again. Second term is "one two" so it's 12.
12
12x(the next prime) = 12x5 = 60

Back to look and say. Third term is "two ones". 21.
21
21x(the next prime) = 21x7 = 147

33 = "two threes" so the next term is 23. Multiply by the next prime (11) and we get 253.

12 = "one one, one two" = 1112. Multiply by 13 to get 14456.

"one six one zero" = 1610. Multiply by 17 = 27370.

"one two one one" = 1211.


Hence the next three terms are 1610, 27370, 1211. Interesting puzzle, it's been a long time since I've seen the "say and see" sequence and that part took by far the longest to figure. The prime number multiplication part should come fairly easily. As Gump says, if you've never seen a "say and see" sequence before you're probably well lost.

</font>