http://en.wikipedia.org/wiki/Persistence_of_a_number

persistence.hs

import Data.List (unfoldr)
import Data.Tuple (swap)
import System.IO (hSetBuffering, stdout, BufferMode(..))

placeValues base = reverse . unfoldr (\x -> if x == 0 then Nothing else Just $ swap $ divMod x base)
persistencePath base x = if x < base then [x] else x : (persistencePath base $ product $ placeValues base x)
persistence base n = length (persistencePath base n) - 1
lowestNumberSuchThat f = head $ dropWhile (not . f) [0..]

main = do
  hSetBuffering stdout NoBuffering
  base <- fmap read $ putStr "base: " >> getLine
  targetPersistence <- fmap read $ putStr "persistence: " >> getLine
  putStrLn $ show $ lowestNumberSuchThat $ \x -> persistence base x == targetPersistence