Números N cuyos cuadrados tienen dos copias de cada dígito de N

5 Comentarios

1. Haskell

   import Data.List especiales :: [Integer] especiales = [y | y <- [1..], doblesCifras y] doblesCifras :: Integer -> Bool doblesCifras n = group (concatMap (replicate 2) (sort (show n))) == group (sort (show (n*n)))

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   import Data.List   especiales :: [Integer] especiales = [y | y <- [1..], doblesCifras y]   doblesCifras  :: Integer -> Bool doblesCifras n =     group (concatMap (replicate 2) (sort (show n))) ==       group (sort (show (n*n)))

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   1. La función doblesCifras puede simplificarse (no es necesario group):

      Haskell

      doblesCifras :: Integer -> Bool doblesCifras n = (sort.concat.replicate 2.show) n == (sort.show) (n^2)

      1 2	doblesCifras :: Integer -> Bool doblesCifras n = (sort.concat.replicate 2.show) n == (sort.show) (n^2)

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2. Haskell

   import Data.List especiales :: [Integer] especiales = filter esEspecial [1..] where esEspecial n = null $ show n \\ (show (n*n) \\ show n)

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   import Data.List   especiales :: [Integer] especiales = filter esEspecial [1..]     where esEspecial n = null $ show n \\ (show (n*n) \\ show n)

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3. Haskell

   especial :: Integer -> Bool especial x = nub (digitosOK x) == nub (digitosOK (x^2)) && aux (x^2) == map (*2) (aux x) where aux x = map (genericLength) (group (digitosOK x)) digitosOK :: Integer -> [Integer] digitosOK n | n >= 10 = sort $ (n `rem` 10) : digitosOK (n`div` 10) | otherwise = [n] especiales :: [Integer] especiales = [ x | x <- [72576..], especial x]

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   especial :: Integer -> Bool especial x = nub (digitosOK x) == nub (digitosOK (x^2)) &&              aux (x^2) == map (*2) (aux x)                  where aux x = map (genericLength) (group (digitosOK x))     digitosOK :: Integer -> [Integer] digitosOK n | n >= 10 = sort $ (n `rem` 10) : digitosOK (n`div` 10)             | otherwise = [n]   especiales :: [Integer] especiales = [ x | x <- [72576..], especial x]

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4. En Maxima

   especiales (n) := block ([k:0, r:[], i:1], while k < n do ( if especial (i) then (r : cons (i,r), k : k+1), i : i+1), reverse (r))$ especial (n) := block([ys], ys : string(n), is (ssort (sconcat(ys,ys)) = ssort (string (n^2))))$ /* (%i15) showtime : true$ Evaluation took 0.0000 seconds (0.0000 elapsed) (%i16) especiales (5); Evaluation took 29.4800 seconds (29.5400 elapsed) (%o16) [72576, 406512, 415278, 494462, 603297] */

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   especiales (n) := block ([k:0, r:[], i:1],   while k < n do     ( if especial (i)       then (r : cons (i,r), k : k+1),       i : i+1),   reverse (r))$    especial (n) := block([ys],   ys : string(n),   is (ssort (sconcat(ys,ys)) = ssort (string (n^2))))$   /*    (%i15) showtime : true$    Evaluation took 0.0000 seconds (0.0000 elapsed)    (%i16) especiales (5);    Evaluation took 29.4800 seconds (29.5400 elapsed)    (%o16) [72576, 406512, 415278, 494462, 603297] */

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