Re-arrange, remove cruft and random primes

src/3n+1/Main.hs

@@ -1,47 +1,55 @@
+{-
+The Simplest Math Problem No One Can Solve - Collatz Conjecture
+https://youtu.be/094y1Z2wpJg
+-}
+
 import           Control.Monad ()
 import           Debug.Trace   (trace)
 
-f' :: Integer -> Integer
-f' n = f'' 0 n
-  where
-    f'' :: Integer -> Integer -> Integer
-    f'' i n'
-      | n' == 1 = t' i
-      | even n' = t $ f'' (i + 1) (n' `div` 2)
-      | odd  n' = t $ f'' (i + 1) (3*n' + 1)
-      where t   = trace ("i: " ++ show i ++ ", number: " ++ show n')
-            t'  = t'' $ trace ("END: " ++ show n ++ ", length: " <> show i) $ t''
-            t'' = trace "\n#######################################################\n"
+main :: IO ()
+main = print $ map f [2^100000..]
 
 f :: Integer -> Integer
-f n = s 0 n
+f n = s 1 n
   where
     s :: Integer -> Integer -> Integer
     s i n
       | n ==    1  = i
-      | even n = s i' (n `div` 2)
-      | odd  n = s i' (3*n + 1)
-      where i' = i + 1
+      | n ==    0  = i
+      | n ==  (-1) = i
+      | n ==  (-5) = i
+      | n == (-17) = i
+      | even n = s (succ i) (n `div` 2)
+      | odd  n = s (succ i) (3*n + 1)
 
-main :: IO ()
-main = print $ map f [2^361..]
+f' :: Integer -> Integer
+f' n = f'' 1 n
+  where
+    f'' :: Integer -> Integer -> Integer
+    f'' i n'
+      | n' ==   1   = t' 0 + t i
+      | n' ==   0   = t' 0 + t i
+      | n' == (-1 ) = t' 0 + t i
+      | n' == (-5 ) = t' 0 + t i
+      | n' == (-17) = t' 0 + t i
+      | even n' = t $ f'' (succ i) (n' `div` 2)
+      | odd  n' = t $ f'' (succ i) (3*n' + 1)
+      where t   = trace ("i: " ++ show i ++ ", number: " ++ show n')
+            t'  = t'' $ trace ("END: " ++ show n ++ ", length: " <> show i) t''
+            t'' = trace "\n#######################################################\n"
 
 -- collatz collect
 -- generate the collatz sequence and return it
-
 cc :: Integer -> [Integer]
 cc n = cc' [] n
   where
     cc' :: [Integer] -> Integer -> [Integer]
     cc' acc n
-      | n == 1 = 1:acc
+      | n ==    1  = acc <>   [1]
+      | n ==    0  = acc <>   [0]
+      | n ==  (-1) = acc <>  [-1]
+      | n ==  (-5) = acc <>  [-5]
+      | n == (-17) = acc <> [-17]
       | even n = cc' acc' (n `div` 2)
       | odd  n = cc' acc' (3*n + 1)
       where acc' = acc <> [n]
-
-primes :: [Integer]
-primes = sieve [2..]
-  where
-    sieve (p:xs) = p : sieve [x|x <- xs, x `mod` p > 0]
-
-isPrime k = (k > 1) && null [ x | x <- [2..k - 1], k `mod` x == 0]