use strict;

open(IN,'old_file.txt') or die;

my $i = 1;
while (<IN>) {
   if (/^(\d+)\s*$/) {
      open(OUT,'>new_file'.sprintf("%02d",$i++).'.txt') or die;
      do { $_ = <IN>; print OUT; } for (1..$1);
   }
}