Welcome to the Monastery, angela2!

The following example will look into a directory specified by $dir, check whether the file name consists of only a series of digits, then adds the full path to @empty_files array, but only if the file is actually empty.

use strict;
use warnings;

my $dir = 'test';

opendir my $dir_handle, $dir or die $!;

my @files = readdir $dir_handle;
my @empty_files;

for my $file (@files){

    my $path = "$dir/$file";

    next if -d $path; # skip if file is a directory

    if ($file =~ /^(\d+)$/){
        next if ! -z $path; # skip if file is not empty
        push @empty_files, $path;
    }
}

for my $file (@empty_files){
    print "$file\n";
}
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