Okay, one more, less obvious connection between 1001 and 9:
Take the multiplicative inverse of the divisors of 1001:
1/7 = 0.142857….(these six digits repeat after that, forever)
1/11 = 0.09…..(repeating)
1/13 = 0.076923,,,,(repeating).
Now add the first half of the repeating digits to the second half (so, for instance: 1+8, 4+5 and 2+7) and you get 9999999…. (infinitely many)
