Self-descriptive numbers

Write a script to display the first three self-descriptive numbers. As per Wikipedia, the definition of Self-descriptive Number is an integer m that in a given base b is b digits long in which each digit d at position n (the most significant digit being at position 0 and the least significant at position b−1) counts how many instances of digit n are in m.

Examples

Example 1
Input: 3
Output: 1210, 2020, 21200

1210 is a four-digit self-descriptive number:
position 0 has value 1 as there's only one 0 in the number
position 1 has value 2 as there are two 1s in the number
position 2 has value 1 as there's only one 2 in the number
position 3 has value 0 as there is no 3 in the number

Analysis

The Wikipedia entry is perhaps overcomplicated in that numbers here are essentially strings of digits rather denoting a value in some base. The definition thus boils down to:

A self-descriptive number is a string of digits in which the d'th digit (counting from 0) is a count of the number of ds in the string.

I therefore looped up from 1, counting the number of each digit 0 to 9 in the string and from that checked whether the number was self-descriptive.

That algorithm found the specified 3 numbers - 1210, 2020 and 21200 in negigible time, found the fourth (3211000) in around 10 seconds and the fifth (42101000) in about 10 minutes. I didn't go any further.

I am sorry that the 'Try it' feature is currently working very slowly or not at all owing to some issue with my web hosting provider.

Try it 

#!/usr/bin/perl

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

use v5.26;    # The Weekly Challenge - 2021-04-05
use utf8;     # Week 107 - task 1 - Self-descriptive numbers
use warnings; # Peter Campbell Smith
binmode STDOUT, ':utf8';
use Encode;

self_descriptive_numbers(3);

sub self_descriptive_numbers {
    
    my ($number, $position, @sd_numbers, @has, $limit, @occurs, $value, $last_index);
    
    # initialise
    $limit = $_[0];
    
    @sd_numbers = ();
    N: for $number (1 .. 1e10) {
        
        # count occurrences of 0 - 9
        $last_index = length($number) - 1;
        @has = (0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
        for $position (0 .. $last_index) {
            $value = substr($number, $position, 1);
            
            # if any digit exceeds the no of digits then this is no good
            next N if $value > $last_index;
            $has[$value] ++;
        }
        
        # check if self_descriptive
        for $position (0 .. $last_index) {
            next N unless substr($number, $position, 1) == $has[$position];
        }
        push @sd_numbers, $number;
        last if @sd_numbers == $limit;
    }
        
    say qq[\nInput:  $limit];
    say qq[Output: ] . join(', ', @sd_numbers);
}

17 lines of code
Completed after the closing date and not submitted to GitHub

Output from script

Input:  3
Output: 1210, 2020, 21200