Use a hash if you want to ignore the duplicates, like this

#!/usr/local/bin/perl
use strict;
use warnings;

my $pattern = qr'^LOC_Os0[1-7]g[0-9]*.[0-9]\s';

# read files
my $hash1 = parse_file('file1.txt');
my $hash2 = parse_file('file2.txt');

# report
my $count=0;
for my $loc (sort keys %$hash1){
  if ( exists $hash2->{$loc} ){
    print "$loc\n";
    ++$count;
  }
}
print "$count unique patterns in both files\n";

# parse file
sub parse_file{
  my $filename = shift;
  my %hash=(); my $count=0;
  open FH,'<',$filename or die "Can't Open $filename\n";
  while ( my $line = <FH> ){
    if ( $line =~ /($pattern)/ ){
      $hash{$1} = 1;
    }  
    ++$count;
  }
  close FH;
  print "$count lines read from $filename\n";
  return \%hash;
}
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poj