Fair bases

Consider integers N and K such that 2 ≤ K ≤ N. Write all the numbers 0 ≤ i As an example, suppose N=4 and K=3. Then the numbers in the list are 00,01,02 and 10. Let us find the score of i=00. The first digit of i appears as the first digit thrice (00,01,02) and the second digit of i appears as second digit twice (00,10). Thus the score of 00 is 3+2=5. An integer K (2 ≤ K ≤ N) is called a fair ba