# Lychrel numbers

*Author: Shlomi Fish*

https://projecteuler.net/problem=55

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.

Source code: prob055-shlomif.p6

#!/usr/bin/raku use v6; sub rsum($x) { return $x + Int($x.flip()); } sub is_palindrome($int) { my $s = Str($int); return $s.flip eq $s; } sub is_lycherel($start) { my $n = rsum($start); for 1 .. 50 -> $i { return False if is_palindrome($n); $n = rsum($n); } return True; } if (False) { say is_palindrome(11); say rsum(13); } say +((1..10000).grep( { is_lycherel($_) }));