8396 = 2 x 2 x 2099.
8396 does not occur in its factorial in base 2 (binary notation) (A093685).
8396 is a number such that it has four 3s in its base 7 representation (A043408).
8396 has four 0s and two 3s in its base 4 representation (A045083).
8396 is the number of 4-bead necklaces labeled with numbers -46 . . . 46 not allowing reversal, with sum zero and first and second differences in -46 . . . 46 (A209008).
Source: What's Special About This Number?