The increasing sequence 1, 5, 6, 25, 26, 30, 31, 125, 126, … consists of all positive integers that can be formed by summing up distinct powers of 5 - from 1 to N presented in increasing order.
That is, 1 = 5^0, 5 = 5^1, 6 = 5^0 + 5^1, etc, etc.

What’s the 100th integer in this sequence?

Convert 100 to binary to get 1100100. Then, take 1100100 in base 5 to get 18775 in base 10. Therefore, the 100th number is 18775.

Posted by Math Man on 2021-10-21 20:25:50