To answer a few more questions:

1. while ((my $line = <INFILE>) && ($line !~ /SEQ.../)) (Removed as per tye's second comment. Just look below - it's better code anyways.)
2. It's Perl, not PERL
3. The regex match operator is =~. The regex not-match operator is !~. It's an atomic 2-character-long operator, not something like += or -=.
4. Rewrite as such:

   while (my $line = <INFILE>)
   {
       # Do a match against the line, grabbing the number.
       my ($num) = $line =~ /SEQRES\s{2,5}(\d)\s/;
   
       # This means that the line didn't meet our requirements
       # as defined by the regex. So, go get the next line.
       # (I added this ... you may not want it, depending on
       # what else you're doing in the loop.)
       next unless defined $num;
   
       # If that number is 2, leave the while loop.
       last if $num == 2;
   
       # Don't chomp unless there's a possibility we'll use it.
       chomp $line;
   
       # If the number is 1, print it to two places.
       if ($num == 1)
       {
           print "$line\n";
           print OUTFILE "$line\n";
       }
   }
   [download]

Make it obvious what the difference is between the two matches. I assigned the difference to $num, which was done via the capture mechanism of regexes. (Look for the parentheses.)

Update: Changed code per tye's comments.

------
We are the carpenters and bricklayers of the Information Age.

The idea is a little like C++ templates, except not quite so brain-meltingly complicated. -- TheDamian, Exegesis 6

Please remember that I'm crufty and crochety. All opinions are purely mine and all code is untested, unless otherwise specified.