Base 36 counter without I or O - counter

Question

we have a requirement to make our serial numbers Base 36 (0-9,A-Z). My initial thought was store the counter in decimal and convert to hex only when required for display. This makes the counting simple, however there is another requirement to not use I or O because it'll be confused with 1 and 0 on the barcodes human readable portion. This makes it a bit of a nightmare.
Language is unimportant, but the counter itself will be held in SQL Server 2012+.
Anyone have any experiences with this problem?
Edit:
I've rewritten a method I found to test in C#. It allows any string of base characters to be passed in.
ie. string baseChars = "0123456789ABCDEFGHJKLMNPQRSTUVWXYZ";
It's not pretty but its a start!
private string GetCustomBase(int iValue, string baseChars)
{
int baseNum = baseChars.Length;
int value= iValue;
string result = "";
while( value > 0 )
{
result = baseChars[ 0 + (value % baseNum)] + result;
value = value / baseNum;
}
return result;
}
private int GetDecimal(string strValue, string baseChars)
{
int baseNum = baseChars.Length;
string strAmendedValue = strValue;
int iResult = 0;
//Each char one at a time (from right)
for (int i = 0; i < strValue.Length; i++)
{
string c = strValue.Substring(strValue.Length - i -1, 1);
int iPos = baseChars.IndexOf(c); //get actual value (0 = 0, A = 10 etc.)
int iPowerVal = (int)Math.Pow((double)baseNum, (double)(i));
iResult = iResult + (iPowerVal * iPos);
}
return iResult;
}

Answer 1

An implementation of the suggestion in the question comments. As language is unimportant, here's a Ruby version:
class Integer
def to_34_IO_shifted
to_s(34).upcase.tr("IJKLMNOPQRSTUVWX", "JKLMNPQRSTUVWXYZ")
end
end
class String
def from_34_IO_shifted
upcase.tr("JKLMNPQRSTUVWXYZIO", "IJKLMNOPQRSTUVWX10").to_i(34)
end
end
puts 170.times.map { |x| x.to_34_IO_shifted }.join(' ')
x = 73644
x34 = x.to_34_IO_shifted
x10 = x34.from_34_IO_shifted
puts "\n#{x} -> '#{x34}' -> #{x10}"
puts "'10' -> #{'10'.from_34_IO_shifted}"
puts "'IO' -> #{'IO'.from_34_IO_shifted}"
Output:
0 1 2 3 4 5 6 7 8 9 A B C D E F G H J K L M N P Q R S T U V W X Y Z 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 1G 1H 1J 1K 1L 1M 1N 1P 1Q 1R 1S 1T 1U 1V 1W 1X 1Y 1Z 20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F 2G 2H 2J 2K 2L 2M 2N 2P 2Q 2R 2S 2T 2U 2V 2W 2X 2Y 2Z 30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F 3G 3H 3J 3K 3L 3M 3N 3P 3Q 3R 3S 3T 3U 3V 3W 3X 3Y 3Z 40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F 4G 4H 4J 4K 4L 4M 4N 4P 4Q 4R 4S 4T 4U 4V 4W 4X 4Y 4Z
73644 -> '1VQ0' -> 73644
'10' -> 34
'IO' -> 34
EDIT: made it so that I and O are interpreted as 1 and 0, in case someone does misread it.