use POSIX;

for ($i = 2; $i <= 10000; $i++) {
  next if (sqrt($i) == int(sqrt($i)));
  
  $n = floor(sqrt($i)); #get the first num
  $found = 0;
  
  $s = sqrt($i);
  $denominator = $s - $n; #decimal value left
  $z = $n; #z = 4
  $numerator = $lastNum = 1;
  
  %seen = ();
  $c = 0;
  while (! $found) {
    $c++;
    $lastNum = $numerator;
	
	$numerator = $numerator * ($s + $z);
    $denominator = sprintf("%.1f",($denominator * ($s + $z))); #this will be an integer
	
	$n = floor($numerator / $denominator); #find over amount
	
	$z = sprintf("%.1f",-1 * (($numerator - $n * $denominator) / $lastNum - $s));
	
	$denominator = sprintf("%.1f",$denominator / $lastNum);
	
	$found = 1 if ($seen{$denominator . ',' . $z . ',' . $lastNum} == 1 && ($c > 1));
	$seen{$denominator . ',' . $z . ',' . $lastNum} = 1 if ($c > 1);
	
	$numerator = $denominator; #flip
	$denominator = $s - $z;
  }
  
  $count++ if ($c > 0 && ($c % 2 == 1));
}

print "Total: $count\n";