An old tactic when faced with a representation that has a lot of boundary cases. Convert to and from a representation that is easier to work with, like so:

use strict;
use Carp;

# Takes a list of months in yyyymm format, returns the gaps in sorted 
+order.
sub find_gaps {
  my @dates = sort {$a <=> $b} map {yyyy_mm2mon_num($_)} @_;
  my $last_mon_count = shift @dates;
  my @gaps;
  foreach my $mon_count (@dates) {
    foreach my $missed (($last_mon_count + 1)..($mon_count-1)) {
      push @gaps, mon_num2yyyy_mm($missed);
    }
    $last_mon_count = $mon_count;
  }
  return @gaps;
}

# Converts a count of months back into yyyymm format
sub mon_num2yyyy_mm {
  my $mon_num = shift;
  use integer;
  my $yyyy = $mon_num / 12;
  my $mm = 1 + $mon_num % 12;
  # Sanity check
  unless (1900 < $yyyy and $yyyy < 2200) {
    carp("Month number '$mon_num' gives a year of $yyyy which seems st
+range");
  }
  return "$yyyy-$mm";
}

# Converts yyyymm format into a count of months from year 0.  (Which d
+idn't
# exist, shoot me.  It is a convenient base-point for calculations.)
sub yyyy_mm2mon_num {
  my $date = shift;
  if ($date =~ /(\d{4}).*?(\d\d?)/) {
    return 12*$1 + $2 - 1;
  }
  else {
    confess("Date '$date' is not in yyyymm format?");
  }
}
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