A HASH makes more sense for this structure:

my ($k,$v, %seq);
for my $line (<DATA>) {
  chomp ($line);
  if ( $line=~/^>(\S+)\s*(.*)/){
     $k=$1;
     $v=$2;
  }else{
     $v=$line;
  }
  $seq{$k} .= $v; 
}
#---- Print it ----
for my $k(sort keys %seq){
  print "$k \t=> $seq{$k}\n";
}
# --- Output ---(Using the __DATA__ block above) ..-
#  123     => blahabcdefghijkl
#  456     => de dahmnopqr
#  789     => nothing wanted herestuvwxyz
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