055_lychrel_numbers.hs

-- If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

-- Not all numbers produce palindromes so quickly. For example,

-- 349 + 943 = 1292,
-- 1292 + 2921 = 4213
-- 4213 + 3124 = 7337

-- That is, 349 took three iterations to arrive at a palindrome.

-- Although no one has proved it yet, it is thought that some numbers, like 196, never produce
-- a palindrome. A number that never forms a palindrome through the reverse and add process is
-- called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose
-- of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition
-- you are given that for every number below ten-thousand, it will either (i) become a palindrome
-- in less than fifty iterations, or, (ii) no one, with all the computing power that exists,
-- has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown
-- to require over fifty iterations before producing a palindrome:
-- 4668731596684224866951378664 (53 iterations, 28-digits).

-- Surprisingly, there are palindromic numbers that are themselves Lychrel numbers;
-- the first example is 4994.

-- How many Lychrel numbers are there below ten-thousand?

import MyLib_haskell

isLychrel :: Int -> Integer -> Bool
isLychrel n = not . or . map isPalindrome . take n . tail . iterate (\x -> x + reverseInt x)

main :: IO()
main = print $ length $ filter (==True) $ map (isLychrel 50) [1..9999]