Sara Reynolds (26 Oct 2011)
"Amazing math patterns of 3's, 6's, and 9's."

Here's the patterns of 3, 6 and 9 and also the repdigits of 3, 6 and 9.

Repeat of 3's and the Multiplication of 34 and 37

3 x 34 = 102  33 x 34 = 1122  333 x 34 = 11322  3333 x 34 = 113322  33333 x 34 = 1133322  333333 x 34 = 11333322
3 x 37 = 111  33 x 37 = 1221  333 x 37 = 12321  3333 x 37 = 123321  33333 x 37 = 1233321  333333 x 37 = 12333321

Repeat of 6's

6 x 34 = 203  66 x 34 = 2233  666 x 34 = 22633  6666 x 34 = 226633  66666 x 34 = 2266633  666666 x 34 = 22666633
6 x 37 = 222  66 x 37 = 2332  666 x 37 = 23632  6666 x 37 = 236632  66666 x 37 = 2366632  666666 x 37 = 23666632

Repeat of 9's

9 x 34 = 306  99 x 34 = 3366  999 x 34 = 33966  9999 x 34 = 339966  99999 x 34 = 3399966  999999 x 34 = 33999966
9 x 37 = 333  99 x 37 = 3663  999 x 37 = 36963  9999 x 37 = 369963  99999 x 37 = 3699963  999999 x 37 = 36999963

Now according to the triangular numbers.... 21 is the 6th triangle, 2211 is the 66th triangle, 222111 is the 666th triangle, 22221111 is the 6666th triangle.