I am looking the way to proceed further in following difficulties. Observe the following:
n = 3 + 3(6) + 3[$6^2$] + 3[$6^3$] ......(1) = 129
Now by writing 129 in base 6, we see the repeated digit 3 up to three times.
If we took one more term 3[$6^3$] in (1), we will get repeated 3 up to 4 times and so on.
Now, my question is, how it is repeated and why this happening like this? is there any reason beside the adding number of terms and having those many threes in base 6.
If we replace 3 by a and 6 by k, for writing n in base k, we get repeated a up to m times, where m is number of terms in (1).