Please feel free to use this function to test any strings produced:

# Will return an analysis of the string.
# Usage: print analyse( $string );
sub analyse {

    # Make an array from the number and create hash.
    my $number = shift;
    my @string = split //, $number;
    my %count  = ();

    # Work over the number adding values to the hash.
    while (1) {
        my $candidate = $string[0].$string[1].$string[2].$string[3];
        $count{$candidate}++;

        # Get rid of first element of the array.
        shift @string;

        # Break out at the end of array.
        last if scalar @string < 4;
    }

    # Tally up the number of duplicates and missing numbers.
    my $duplicates = 0;
    my $missing    = 0;

    for ( 0 .. 9999 ) {
        my $k = 0 x ( 4 - length $_ ) . $_;
        my $v = $count{$k};
        unless ( defined $v ) {
            $missing++;
            next;
        }
        $duplicates += ( $v - 1 ) if $v > 1;
    }

    # Create the summary.
    my $text;
    $text .= "      Length is: " . length($number) . "\n";
    $text .= "  Missing count: " . $missing . "\n";
    $text .= "Duplicate count: " . $duplicates . "\n\n";

    return $text;
}
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