EA: "Are all integers potential hits?" No, only a few. Because a hit involves only as many digits as one's starting number (call it d), after an accumulation and concatenation just drop any digits after the first d. This shortcut creates a finite space and numbers traversing it will necessarily loop. But the loop, i.e. the eventually repeated term, is not likely the first term but rather some number subsequent to it. There are 29 two-digit integers that hit. Perhaps surprisingly, each of these may be evolved into a three-digit integer that hits by appending one specific digit. Each of these in turn may be evolved into a four-digit integer that hits by (again) appending a specific digit. And so on. If that holds true, then these 29 100-digit numbers http://chesswanks.com/num/twenty-nine.txt encapsulate all 2-to-100-digit solutions simply by reading the prescribed number of digits left to right.