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?

NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.



In [16]:

    
open System 
open System.Numerics

let rev (str:string) =
    let strArrayRev = str.ToCharArray() |> Array.rev
    String.Join("", strArrayRev)

let addRev n =
    n + BigInteger.Parse(rev(string(n)))

let isPalindrome n = string(n) = rev(string(n))

let rec isLychrel' n i =
    if i > 50I then true
    else
        if i > 0I && isPalindrome n then false
        else isLychrel' (addRev n) (i + 1I)

let isLychrel n =
    isLychrel' n 0I
    
seq { 1I..10000I }
|> Seq.filter isLychrel
|> Seq.length









    Out[16]:





249