Task — Lychrel number

You are given a number, 10 <= $n <= 1000. Write a script to find out if the given number is a Lychrel Number.

To keep the task simple, we impose the following rules: a. Stop if the number of iterations reached 500. b. Stop if you end up with number >= 10_000_000.

Examples

Example 1
Input: $n = 56
Output: 0
After 1 iteration, we found palindrome number.
56 + 65 = 121

Example 2
Input: $n = 57
Output: 0
After 2 iterations, we found palindrome number.
 57 +  75 = 132
132 + 231 = 363

Example 3
Input: $n = 59
Output: 0
After 3 iterations, we found palindrome number.
 59 +  95 =  154
154 + 451 =  605
605 + 506 = 1111

Analysis

This is a rather futile challenge, as no number has yet been proved to be a Lychrel Number. However ...

My non-solution does what is required, and by increasing Muhammad's limit of 10**7 to 10**13 I can show that 89 does and 196 doesn't converge to a palindrome.

According to Wikipedia, 1000206827388999999095750 takes 293 iterations to reach a 132 digit palindrome, and that's well into BigInt territory.

Try it 

#!/usr/bin/perl

# Blog: http://ccgi.campbellsmiths.force9.co.uk/challenge

use v5.26;    # The Weekly Challenge - 2021-11-01
use utf8;     # Week 137 - task 2 - Lychrel number
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';

my $i;
for $i (80 .. 89) {
    lychrel_number($i);
}
lychrel_number(196);

sub lychrel_number {
    
    my ($input, $i, $r, $test);
    $input = shift;
    say qq[\nInput: $input];
    $test = $input;
    
    # iterate up to 500 times
    for $i (0 .. 499) {
        $r = reverse($test);
        
        # found a palindrome
        if ($r == $test) {
            print qq[Output: $input is not a Lychrel Number - ];
            say qq[$r reached after $i iterations];
            return;
        }
        # not a palindrome so add and repeat
        $test += $r;
        
        # reached a very large number so give up
        if ($test >= 10_000_000_000_000) {
            say qq[Output: 1 - reached $test after $i iterations];
            return;
        }
    }

    # like it says
    if ($r != $test) {
        say qq[Output: still not palindromic after 500 iterations];
        
    # but no number has yet been shown to be one    
    } else {
        say qq[Output: $input is a Lychrel Number];
    }
}

Output

Input: 80
Output: 80 is not a Lychrel Number - 88 reached after 1 iterations

Input: 81
Output: 81 is not a Lychrel Number - 99 reached after 1 iterations

Input: 82
Output: 82 is not a Lychrel Number - 121 reached after 2 iterations

Input: 83
Output: 83 is not a Lychrel Number - 121 reached after 1 iterations

Input: 84
Output: 84 is not a Lychrel Number - 363 reached after 2 iterations

Input: 85
Output: 85 is not a Lychrel Number - 484 reached after 2 iterations

Input: 86
Output: 86 is not a Lychrel Number - 1111 reached after 3 iterations

Input: 87
Output: 87 is not a Lychrel Number - 4884 reached after 4 iterations

Input: 88
Output: 88 is not a Lychrel Number - 88 reached after 0 iterations

Input: 89
Output: 89 is not a Lychrel Number - 8813200023188 reached after 24 iterations

Input: 196
Output: 1 - reached 17602285712176 after 25 iterations