Let AOD(i) be the sum of digits of i divided by the number of digits of i, or the Average Of Digits.
N is the smallest integer > 1 such that the AOD(N^k) is the same for k in {1,2,3,4}
M has the same requirements as N, except AOD(M) must be an integer.
L has the same requirements as M, except that L is the smallest such integer with AOD(L) equal to some integer other than AOD(M).
Find:
1. N, AOD(N)
2. M, AOD(M)
3. L, AOD(L)
Both solvers found N and M, which have the same value for AOD(), which turns out to be 3.
But what is sought in part 3 is the smallest integer raised to each of the powers 1,2,3,4 has an AOD which is an integer but which some integer OTHER than 3.

Posted by Larry
on 20200821 06:53:13 