Strange sequence of numbers

I recently noticed that dividing
a group of 3 consecutive single-digit
numbers by 3, resulted in the following
sequence.

411 522 633 744 855 966 ...

And when multiplied by three,

411 5 * 3 = 12345

411 522 6 * 3 = 12345678

411 522 633 7 * 3 = 123456789011

411 522 633 744 8 * 3 = 12456789012344