I think what you want is reading 16 lines in a gulp not every 16th line.

UPDATE:

more explicit:

while ( @lines = readlines($filehandle,16) ) {
  print @lines,"----\n";
}
 
sub readlines {
  my ($fh, $count) = @_;
  my @gulp;
  while (<$fh>) {
    push @gulp,$_;
    last unless --$count;
  }
  return @gulp;
}
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