Cadenas de primos complementarios

PorJosé A. Alonso 30-mayo-201625-abril-2021

El complemento de un número positivo x se calcula por el siguiente procedimiento:

si x es mayor que 9, se toma cada dígito por su valor posicional y se resta del mayor los otro dígitos. Por ejemplo, el complemento de 1448 es 1000 – 400 – 40 – 8 = 552. Para
si x es menor que 10, su complemento es x.

Definir las funciones

   cadena    :: Integer -> [Integer]
   conCadena :: Int -> [Integer]

1 2	cadena :: Integer -> [Integer] conCadena :: Int -> [Integer]

tales que

(cadena x) es la cadena de primos a partir de x tal que cada uno es el complemento del anterior. Por ejemplo,

     cadena 8         == []
     cadena 7         == [7]
     cadena 13        == [13,7]
     cadena 643       == [643,557,443]
     cadena 18127     == [18127,1873,127,73,67,53,47]
     cadena 18181213  == [18181213,1818787,181213,18787,1213,787,613,587]

cadena 8 == []

cadena 7 == [7]

cadena 13 == [13,7]

cadena 643 == [643,557,443]

cadena 18127 == [18127,1873,127,73,67,53,47]

cadena 18181213 == [18181213,1818787,181213,18787,1213,787,613,587]

(conCadena n) es la lista de números cuyas cadenas tienen n elementos. Por ejemplo,

     take 6 (conCadena 3)                == [23,31,61,67,103,307]
     [head (conCadena n) | n <- [4..8]]  == [37,43,157,18127,181873]

1 2	take 6 (conCadena 3) == [23,31,61,67,103,307] [head (conCadena n) \| n <- [4..8]] == [37,43,157,18127,181873]

Soluciones

[schedule expon=’2016-06-06′ expat=»06:00″]

Las soluciones se pueden escribir en los comentarios hasta el 06 de junio.
El código se debe escribir entre una línea con <pre lang=»haskell»> y otra con </pre>

[/schedule]

[schedule on=’2016-06-06′ at=»06:00″]

import Data.Numbers.Primes

cadena :: Integer -> [Integer]
cadena x    
    | x < 10 && isPrime x = [x]
    | otherwise           = takeWhile isPrime (iterate f x)
    where f x | x < 10 && isPrime x = 0
              | otherwise           = complemento x

complemento :: Integer -> Integer
complemento x = (div x c)*c - (rem x c)
    where c = 10^(length (show x) - 1)          

conCadena :: Int -> [Integer]
conCadena n =
    [y | y <- primes, length (cadena y) == n]

import Data.Numbers.Primes

cadena :: Integer -> [Integer]

cadena x

| x < 10 && isPrime x = [x]

| otherwise = takeWhile isPrime (iterate f x)

where f x | x < 10 && isPrime x = 0

| otherwise = complemento x

complemento :: Integer -> Integer

complemento x = (div x c)*c - (rem x c)

where c = 10^(length (show x) - 1)

conCadena :: Int -> [Integer]

conCadena n =

[y | y <- primes, length (cadena y) == n]

[/schedule]

3 Comentarios

import Data.Numbers.Primes


cadena    :: Integer -> [Integer]
cadena x | isPrime x && x>9  = x : cadena(resta(desc x))
         | isPrime x && x<=9 = [x]
         | otherwise         = []

conCadena :: Int -> [Integer]
conCadena n = [x | x <- [1..], length (cadena x) == n]


resta :: Num t => [t] -> t
resta [x]    = x
resta (x:xs) = x - sum(xs)

desc :: Integer -> [Integer]
desc x = [z*10^(n-1) | (z,n) <- zip (leer x) [length (leer x), (length (leer x))-1..1]]

leer :: Integer -> [Integer]
leer x = [read [z] | z <- show x]

import Data.Numbers.Primes

cadena :: Integer -> [Integer]

cadena x | isPrime x && x>9 = x : cadena(resta(desc x))

| isPrime x && x<=9 = [x]

| otherwise = []

conCadena :: Int -> [Integer]

conCadena n = [x | x <- [1..], length (cadena x) == n]

resta :: Num t => [t] -> t

resta [x] = x

resta (x:xs) = x - sum(xs)

desc :: Integer -> [Integer]

desc x = [z*10^(n-1) | (z,n) <- zip (leer x) [length (leer x), (length (leer x))-1..1]]

leer :: Integer -> [Integer]

leer x = [read [z] | z <- show x]

Responder

import Data.Numbers.Primes

complemento :: Integer -> Integer
complemento x = (div x c)*c - (rem x c)
              where c = 10^(length (show x) - 1)          

cadena :: Integer -> [Integer]
cadena x | isPrime x = x:aux x
         | otherwise = []
         where aux x | x < 10 = []
                     | isPrime x && isPrime c = c:aux c
                     | otherwise = []
                     where c = complemento x

conCadena :: Int -> [Integer]
conCadena n = filter (\x -> n==length (cadena x)) [1..]

import Data.Numbers.Primes

complemento :: Integer -> Integer

complemento x = (div x c)*c - (rem x c)

where c = 10^(length (show x) - 1)

cadena :: Integer -> [Integer]

cadena x | isPrime x = x:aux x

| otherwise = []

where aux x | x < 10 = []

| isPrime x && isPrime c = c:aux c

| otherwise = []

where c = complemento x

conCadena :: Int -> [Integer]

conCadena n = filter (\x -> n==length (cadena x)) [1..]

Responder

Solución simplificada eliminando «isPrime x» de la segunda guarda de «aux»:

import Data.Numbers.Primes

complemento :: Integer -> Integer
complemento x = (div x c)*c - (rem x c)
              where c = 10^(length (show x) - 1)          

cadena :: Integer -> [Integer]
cadena x | isPrime x = x:aux x
         | otherwise = []
         where aux x | x < 10 = []
                     | isPrime c = c:aux c
                     | otherwise = []
                     where c = complemento x

conCadena :: Int -> [Integer]
conCadena n = filter (\x -> n==length (cadena x)) [1..]

import Data.Numbers.Primes

complemento :: Integer -> Integer

complemento x = (div x c)*c - (rem x c)

where c = 10^(length (show x) - 1)

cadena :: Integer -> [Integer]

cadena x | isPrime x = x:aux x

| otherwise = []

where aux x | x < 10 = []

| isPrime c = c:aux c

| otherwise = []

where c = complemento x

conCadena :: Int -> [Integer]

conCadena n = filter (\x -> n==length (cadena x)) [1..]

Responder

Cadenas de primos complementarios

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