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import Data.List digits b = reverse . map (`mod` b) . takeWhile (> 0) . iterate (`div` b) undigits b = foldl' (\a b -> b * a + b) 0 step b = sum . map (^2) . digits b untilCycle f x = reverse $ go x [] where go x xs | x `elem` xs = x : xs | otherwise = go (f x) (x:xs) getCycle f x = dropWhile (/= last xs) xs where xs = untilCycle f x showChain b = untilCycle (step b) reaches b = minimum . getCycle (step b) allReached b = nub $ map (reaches b) [1 .. b^4]
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