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+
+
+
+isInt :: (RealFrac a) => a -> Bool
+isInt x =
+    x == fromInteger (round x)
+
+
+
+modulo :: Int -> Int -> Int
+modulo x y =
+    x - (x `div` y) * y
+
+
+
+primeFactors :: Int -> [Int]
+primeFactors x =
+    let p = (\x e c -> if (x == 1)
+                       then (reverse c)
+                       else if (x `modulo` (head e) == 0)
+                            then p (x `div` (head e)) e ((head e) : c)
+                            else p x (tail e) c)
+    in p x euler []
+
+
+
+euler :: [Int]
+euler =
+    let f = (\list -> (head list) : (f (filter (\x -> x `modulo` (head list) /= 0) list)))
+    in f [2..]
+
+
+
+isPowerOf :: Int -> Int -> Bool
+isPowerOf x y =
+    case (compare x y) of
+        LT -> False
+        EQ -> True
+        GT -> if (x `modulo` y == 0) then isPowerOf (x `div` y) y else False
+
+
+
+-- some simple fractran programs
+
+-- input: 2^a * 3^b
+-- output: 3^(a+b)
+addition :: [(Int,Int)]
+addition = [(3,2)]
+
+-- input: 2^a * 3^b
+-- output: 5^ab
+multiply :: [(Int,Int)]
+multiply = [(13,21), (385,13), (1,7), (3,11), (7,2), (1,3)]
+
+-- input: 2
+-- output: a sequence containing all prime powers of 2
+prime2 :: [(Int,Int)]
+prime2 = [(17,91), (78,85), (19,51), (23,38), (29,33), (77,29), (95,23), (77,19), (1,17), (11,13), (13,11), (15,14), (15,2), (55,1)]
+
+-- input: 10
+-- output: a sequence containing all prime powers of 10
+prime10short :: [(Int,Int)]
+prime10short = [(3,11), (847,45), (143,6), (7,3), (10,91), (3,7), (36,325), (1,2), (36,5)]
+
+prime10 :: [(Int,Int)]
+prime10 = [(7,3), (99,98), (13,49), (39,35), (36,91), (10,143), (49,13), (7,11), (1,2), (91,1)]
+
+
+
+fractran :: [(Int,Int)] -> Int -> [Int]
+fractran program value =
+    let prog = map (\(x,y) -> (fromIntegral x, fromIntegral y)) program
+        f = (\p v -> if (p == [])
+                     then []
+                     else let (curX, curY) = head p
+                              newV = v * curX / curY
+                          in if (isInt newV)
+                             then newV : (f prog newV)
+                             else f (tail p) v)
+        result = map round (f prog (fromIntegral value))
+    in value : result
+
+
+