ProSum Numbers are obtained when the product of an integer's digits divided by the sum of its digits is itself an integer. If the resultant integer can be used to produce yet another integer in the same way, a sequence is formed. It is terminated when a new term is less than 10. The first term must be at least 10, or an endless loop is formed.

Find the lowest starting term for a sequence of two ProSum Numbers, then do the same for three terms and four terms.

I found a few but am not sure if I have the lowest.

Two term sequences:
10 -> 0
22 -> 1
36 -> 2

Three term sequences:
666666 -> 1296 -> 6
7777777 -> 16807 -> 0
333333333 -> 729 -> 7

Four term sequence:
twenty-seven 3's -> 94143178827 -> 50176 -> 0

Posted by Jer on 2015-01-28 11:25:10