9! = 362880 is the smallest factorial that begins with 3, so a(1) = 9.
62! = 314699..., whose first 3 digits are 314; no integer less than 62 has 314 as the first 3 digits of its factorial, no does any integer less than 62 have 31 as the first 2 digits of its factorial, so a(2) = a(3) = 62.
