mystery sequence (easy?)

[Ray Chandler]

It does appear to be a table with the n-th row consisting of some number of consecutive n-almost primes:

1: 2,3
2: 9,10,
3: 27,28,30,
4: 81,84,88,90,100,104,
5: 243,252,264,270,272,280,300,304,312,
6: 729,736,756,784,792,810,816,840,880,900,912,928,936,992,1000,1040,
7: 2187,2208,2268,2352,2368,2376,...

1: A000040(1,2)
2: A001358(3,4)
3: A014612(5..7)
4: A014613(8..13)
5: A014614(14..22)
6: A046306(23..38)
7: A046308(39..??)

Row n starts with the (k+1)st n-almost prime, where k is the number of terms in all the preceding rows.  
After the first row, the starting term is 3^n, but that pattern may not continue.

I don't see a pattern yet to the number of terms in a row {2,2,3,6,9,16,...}.
Ray Chandler