Generating unique 6 digit code

Question

I'm generating a 6 digit code from the following characters. These will be used to stamp on stickers.
They will be generated in batches of 10k or less (before printing) and I don't envisage there will ever be more than 1-2 million total (probably much less).
After I generate the batches of codes, I'll check the MySQL database of existing codes to ensure there are no duplicates.

// exclude problem chars: B8G6I1l0OQDS5Z2

$characters = 'ACEFHJKMNPRTUVWXY4937';

$string = '';

for ($i = 0; $i < 6; $i++) {
    $string .= $characters[rand(0, strlen($characters) - 1)];
}   

return $string;

1. Is this a solid approach to generating the code?
2. How many possible permutations would there be? (6 Digit code from pool of 21 characters). Sorry math isn't my strong point

Answer 1

21^6 = 85766121 possibilities.

Using a DB and storing used values is bad. If you want to fake randomness you can use the following:

Reduce to 19 possible numbers and make use of the fact that groups of order p^k where p is an odd prime are always cyclic.

Take the group of order 7^19, using a generator co-prime to 7^19 (I'll pick 13^11, you can choose anything not divisible by 7).

Then the following works:

$previous = 0;

function generator($previous)
{

  $generator = pow(13,11);
  $modulus = pow(7,19); //int might be too small
  $possibleChars = "ACEFHJKMNPRTUVWXY49";

  $previous = ($previous + $generator) % $modulus;
  $output='';
  $temp = $previous;

  for($i = 0; $i < 6; $i++) {
    $output += $possibleChars[$temp % 19];
    $temp = $temp / 19;
  }

  return $output;
}

It will cycle through all possible values and look a little random unless they go digging. An even safer alternative would be multiplicative groups but I forget my math already :(