I would probably use LWP::Simple to verify that the link exists.

use strict;
use warnings;

use LWP::Simple;

my $data_out_file = $ARGV[0] || 'links.txt';

open my $out_handle, '>', $data_out_file
    or die $!;

for my $index ( 0000 .. 1000 ) {
    my $serial = sprintf "%04s", $index;
    my $site = qq(http://somewebsite/65081$serial.jpg);

    sleep 1;

    next unless head( $site );

    my $link =   qq(<img src = ")
               . $site
               . qq(">);
    print $out_handle 
          $link, "\n";
}

close $out_handle or die $!;
[download]

The head() function grabs the document header, which should tell you if it exists or not. In scalar context it simply returns true if successful.

Update: Added sleep 1; to throttle how quickly you'll be hitting the site. It now will take your script 1000 seconds to execute (almost 17 minutes) but you will avoid overloading the remote server. ...always best to play nice.

$num = '0000';
for(1..1000) {
  print ++$num,"\n";
}
[download]

To your main question, in order to discover whether these JPGs actually exist, why not just download them since you want to look at them anyway, and for that you should find LWP::Simple's getstore() handy. If you really don't want to download them, then just use the head() function to see what the server will offer for each filename, and act accordingly.

One more thing, you should really make a habit of using the 3-arg version of open.

Update: Yes of course, silly me!

Update 2: In response to rodion's excellent question, I did a little reading and my interpretation is that at least for HTML 1.1, the HEAD should return exactly what a simple GET returns, minus the message body content. That implies (to the optimist in me at least) that the HEAD should not return if the GET would not. In fact, in section 9.4 (page 53 of RFC 2616), it notes that HEAD is often used for testing link validity. It would seem that for compliant servers at least, using HEAD should work. Corrections or clarifications are welcome!

$num = '0000';
for(1..1000) {
  print ++$num,"\n";
}
[download]

Or even

for my $num ('0000' .. '1000') {
    ...
}
[download]

If you set this before you issue a "$ua->get( $url )" request, you should be able to check for a "Client-Aborted" header in the response, as per the documentation.

Setting a maximum size allows you to make sure that you could get the document, without the program having to hang around waiting for the whole transfer. If you have a successful transfer, or a "Client-Aborted" header, you know that the link works and you can quickly move on to checking the next one.

Addendum: I just saw Albannach's suggestion for getting the header alone. Does anyone reading this know if there are cases (worth checking for) where you can get the header and can't get the content? If no one knows of any that are relevant to the OP, then just checking the header should be faster than getting a limited amount of content.

I remember downloading from a picture web-site a number of pictures with almost sequentially numbered files. Everytime you hit a "missing" number you got a "This picture does not exist page", so checking for some available content would not have worked. Perhaps only checking for a header could have warned me for the "missing" numbers.

CountZero

"If you have four groups working on a compiler, you'll get a 4-pass compiler." - Conway's Law