In addition to what Eily wrote, please bear in mind that this is PerlMonks and not BioMonks: what's a k-mer?

A consultation of Wikipedia turned up this. IIUC, the 25-base sequence  GGGGGGGGGGGGGGGGGGGGGGGGG has three overlapping 23-base k-mers ending in GG: the 23-base substrings starting at offsets 0, 1 and 2.

The cannonical regex approach to extracting overlapping patterns is this:

c:\@Work\Perl\monks\pearllearner315>perl -wMstrict -le
"my $seq = 'CCCAAAAAAAAAAAAAAAAAAAAAGGTTGGCCGGAAA';
 my @k_mers = $seq =~ m{ (?= (.{21} GG)) }xmsg;
 print qq{'$_'} for @k_mers;
"
'AAAAAAAAAAAAAAAAAAAAAGG'
'AAAAAAAAAAAAAAAAAGGTTGG'
'AAAAAAAAAAAAAGGTTGGCCGG'
[download]

You want only unique k-mers and only the first thousand. One approach (assuming you have already extracted the entire, contiguous base sequence from each FASTA record):

c:\@Work\Perl\monks\pearllearner315>perl -wMstrict -le
"my $seq = 'GGGGGGGGGGGGGGGGGGGGGGGGGGGCCCAAAAAAAAAAAAAAAAAAAAAGGTTGGC
+CGGAAA';
 ;;
 my $rx_kmer = qr{ .{21} GG }xms;
 ;;
 my @k_mers;
 my %seen;
 ;;
 KMER:
 while ($seq =~ m{ (?= ($rx_kmer)) }xmsg) {
   push @k_mers, $1 unless $seen{$1}++;
   last KMER if @k_mers >= 1000;
   }
 ;;
 print qq{'$_'} for @k_mers;
"
'GGGGGGGGGGGGGGGGGGGGGGG'
'AAAAAAAAAAAAAAAAAAAAAGG'
'AAAAAAAAAAAAAAAAAGGTTGG'
'AAAAAAAAAAAAAGGTTGGCCGG'
[download]

Update 1: Eliminated entirely unnecessary  $count variable from final code example.

Update 2: Here's a slightly more elegant approach if you're not going to be extracting millions of k-mers (see List::MoreUtils::uniq):

c:\@Work\Perl\monks\pearllearner315>perl -wMstrict -le
"use List::MoreUtils qw(uniq);
 ;;
 my $seq = 'GGGGGGGGGGGGGGGGGGGGGGGGGGGCCCAAAAAAAAAAAAAAAAAAAAAGGTTGGC
+CGGAAA';
 ;;
 my $rx_kmer = qr{ .{21} GG }xms;
 ;;
 my @k_mers = uniq $seq =~ m{ (?= ($rx_kmer)) }xmsg;
 $#k_mers = 999 if $#k_mers >= 1000;
 ;;
 print qq{'$_'} for @k_mers;
"
'GGGGGGGGGGGGGGGGGGGGGGG'
'AAAAAAAAAAAAAAAAAAAAAGG'
'AAAAAAAAAAAAAAAAAGGTTGG'
'AAAAAAAAAAAAAGGTTGGCCGG'
[download]

Update 3: If you also need the offset of each extracted k-mer subsequence, there are ways to do that, too.