How many bitcoins have been sent to Base58-invalid addresses? Some bitcoins have been permanently lost when they are sent the the following addresses.  The explanation I've found is that they contain characters that are invalid in Base58


1BitcoinEaterAddressDontSendf59kuE
1Boxo846yTDLHgKM94aYseHBnCjJ4eYbzb


Specifically, base58 only allows the following characters  (excluding 0oiL)

static const char* pszBase58 = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"; 


What is the current running total of "lost" bitcoins, or lacking that, what is the general process needed to figure this out?

(What API methods would you call to get the data to determine this?)
The characters excluded in Base58 are 0OIl. oiL are allowed, making these two valid addresses.

It is impossible to send to an invalid address, as Bitcoin transaction scripts actually include raw 160-bit hashes (which by definition have a one-to-one correspondence with valid addresses), not addresses. Bitcoin clients will simply refuse to do anything if an invalid address is given.

There is probably no problem with 1Boxo846yTDLHgKM94aYseHBnCjJ4eYbzb. The problem with 1BitcoinEaterAddressDontSendf59kuE is that, given an English dictionary, it has very low Kolmogorov complexity, making it extremely unlikely that anyone has a private key (or even a public key) for it.

Likewise, 1111111111111111111114oLvT2 is known to correspond to the public key hash 0, which is so simple it is again extremely unlikely anyone has the keys for it.