# Euler Problem 95 – Recursion

After I got this one, I went to the Euler Project problem thread and wanted to read up on what other Haskellers had done. I found lots of posted Haskell routines that make the solution overly complicated, and look like spaghetti. My solution is made of nice and pretty code.

This problem I stared at for a long time. Its not a very difficult problem, but it can really only be solved recursively using native Haskell code. I will not use any mutable arrays. So this is really my first recursive routine. Admittedly, I ball-parked the upper limit to 15K, and got the answers on the first try. This routine runs on an old PC in under a minute.

``` ```
``````sumdiv :: Integer -> Integer
sumdiv n = sum \$ 1 : filter ((== 0) . rem n) [2 .. n `div` 2]

build :: [Integer] -> [Integer]
build chain
| (last chain) == 1 = []
| (last chain) > 1000000 = []
| (last chain) `elem` (init chain) = chain
| otherwise = build (chain ++ [sumdiv (last chain)])

main = print \$ snd \$ maximum [(length c, minimum c) | n<-[12496..15000], let c=build [n], c /= []]
``````