use strict;
use bignum;

my $y; 
my $x;
my $z; 
my $d; 
my $k; 
my $old_z;
my $sum;
my $lim;

$x = 1;

$y = 5;   #2
$z = 13;   #5
$old_z = $z;
$sum = $z;

open(OUT,">digits.txt");

for($k=2; $k<10001; $k++) { 
  if ($z < 2*$y) {
    $y = 4*$y - 2*$z;
    $z = 2*$z + 3;
  } else {
    $y = 4*$y;
    $z = 2*$z-1;
  }
  $d = $z - 2*$old_z +1;
  $old_z = $z;
  $lim=$z - $sum; # + ($k-2);
  $sum=$sum+$z;

  if ($k%100 == 0) { print OUT "$k\t$d\t$lim\n";  select()->flush(); }
}
close(OUT);