What is the smallest positive integer N in which you can "see" the consecutive digits of other integers t, f, and s where:

- the digits of N are all unique
- t=i^3, f=j^4, and s=k^7 for some integers i,j,k
- t, f, and s are each at least 3 digits
- there can be overlap of some of the digits of each of the powers as they appear in N.

For example, if N is abcdefg, then a valid solution would be if abcd, cde, and defg were a perfect cube, a 4th power and a 7th power in some order.
Furthermore, if a number's digits are abcd, then it is included in xyabcdz but not included in xabycdz.

781256

Posted by Steve Herman on 2022-01-10 12:28:06