Divisibility in base $7$ problem Find all integers between $0 \leq a \leq 2400$ such they are divisible by $8$ and that their base 7 development has at least $3$ equal digits.

Hint:  As $7^4=2401$ the numbers $a$ have at most four digits in base $7$, three of which must be equal.  The divisibility test for $11$ in base $10$ (add up the even places and subtract the odd places) is actually a test for $b+1$ in base $b$, so will give you an easy check for divisibility by $8$.  There not many numbers to check.
