Ruth-Aaron numbers: Difference between revisions

</pre>

=={{header|Haskell}}==

<lang haskell>import qualified Data.Set as S

import Data.List.Split ( chunksOf )

divisors :: Int -> [Int]

divisors n = [d | d <- [2 .. n] , mod n d == 0]

--for obvious theoretical reasons the smallest divisor of a number bare 1

--must be prime

primeFactors :: Int -> [Int]

primeFactors n = snd $ until ( (== 1) . fst ) step (n , [] )

where

step :: (Int , [Int] ) -> (Int , [Int] )

step (n , li) = ( div n h , li ++ [h] )

where

h :: Int

h = head $ divisors n

primeDivisors :: Int -> [Int]

primeDivisors n = S.toList $ S.fromList $ primeFactors n

solution :: (Int -> [Int] ) -> [Int]

solution f = snd $ until ( (== 30 ) . length . snd ) step ([2 , 3] , [] )

where

step :: ([Int] , [Int] ) -> ([Int] , [Int])

step ( neighbours , ranums ) = ( map ( + 1 ) neighbours , if (sum $ f

$ head neighbours ) == (sum $ f $ last neighbours) then

ranums ++ [ head neighbours ] else ranums )

formatNumber :: Int -> String -> String

formatNumber width num

|width > l = replicate ( width -l ) ' ' ++ num

|width == l = num

|width < l = num

where

l = length num

main :: IO ( )

main = do

let ruth_aaron_pairs = solution primeFactors

maxlen = length $ show $ last ruth_aaron_pairs

numberlines = chunksOf 8 $ map show ruth_aaron_pairs

ruth_aaron_divisors = solution primeDivisors

maxlen2 = length $ show $ last ruth_aaron_divisors

numberlines2 = chunksOf 8 $ map show ruth_aaron_divisors

putStrLn "First 30 Ruth-Aaaron numbers ( factors ) :"

mapM_ (\nlin -> putStrLn $ foldl1 ( ++ ) $ map (\st -> formatNumber (maxlen + 2) st )

nlin ) numberlines

putStrLn " "

putStrLn "First 30 Ruth-Aaron numbers( divisors ):"

mapM_ (\nlin -> putStrLn $ foldl1 ( ++ ) $ map (\st -> formatNumber (maxlen2 + 2) st )

nlin ) numberlines2</lang>

{{out}}

<pre>First 30 Ruth-Aaaron numbers ( factors ) :

5 8 15 77 125 714 948 1330

1520 1862 2491 3248 4185 4191 5405 5560

5959 6867 8280 8463 10647 12351 14587 16932

17080 18490 20450 24895 26642 26649

First 30 Ruth-Aaron numbers( divisors ):

5 24 49 77 104 153 369 492

714 1682 2107 2299 2600 2783 5405 6556

6811 8855 9800 12726 13775 18655 21183 24024

24432 24880 25839 26642 35456 40081