Brazilian numbers

A number is said brazilian if it can be written with the same 'digit' for some base (0 < digit < base).

For instance, the following numbers are brazilian:
$2222=(2,2,2,2{)}_{10}$
$1281=(7,7,7{)}_{13}$
$33500852988=(127,127,127,127{)}_{641}$

How many brazilian numbers $\le 100,000,000,000$ are there?
[We consider only numbers with at least 3 'digits']

You are given:
$114\text{ numbers}\le 1,000$
$617\text{ numbers}\le 10,000$
$3016\text{ numbers}\le 100,000$
$14387\text{ numbers}\le 1,000,000$

[My timing: 4.7 sec]