More Project fucking Euler

I am proceeding with my attempt at Project Euler Problem #254. It revolves around reversing functions. g(i) is basically the reverse of sf(n). What I am doing is taking an Integer (i) and returning every number k with the following property: If one adds up the digits in k, one comes up with i. Here is my code so far (see if you can spot the obvious error before I continue!):

(Project Euler Problem...)

listToInteger :: [Integer] -> Integer listToInteger xs = listToInteger’ $ reverse xs where listToInteger’ [] = 0 listToInteger’ (x:xs) = x + 10 * listToInteger’ xs

integersAddToInteger :: Int -> [Integer] integersAddToInteger i = sort . map listToInteger . digitsAddTo . take i $ cycle [1]

digitsAddTo :: [Integer] -> Integer digitsAddTo [] = [] digitsAddTo [x] = x digitsAddTo xs = thirdSet xs ++ secondSet xs where secondSet xs = digitsAddTo $ [first xs] ++ rest xs thirdSet (x:xs) = map (x:) . digitsAddTo $ xs first (a:b:xs) = a + b rest (a:b:xs) = xs

(Integer)
(x)

When I call, for example, integersAddToInteger 5, I get this:

[5,14,23,32,41,113,122,131,212,221,311,1112,1121,1211,2111,11111]

Now, the obvious error is that if I want to find all k for an i greater than 9, the function digitsAddTo will begin using double digit numbers. I shall now attempt to fix this problem.