Identical-digit blocks in decimal representation of partition numbers

[Jonathan Post]

This is a dumb base thing to do, but...

scanning njas' b-list for partition number
http://www.research.att.com/~njas/sequences/b000009.txt
I notice these smallest k such that P(k), base 10, has n consecutive
identical digits:

n=1: P(0) = 1
n=2: P(14) = 22
n=3: P(28) = 222
n=4: P(331) = 519999315040
n=5: P(1518) = 3816666699150439747483571506
n=6: ???

Others with blocks of 4 identical digits include:
P(636) has 1^4
P(711) has 8^4
 P(750) has 8^4
 P(948) has 8^4
 P(1143) has 9^4
 P(1273) has 1^4
 P(1583) has 7^4
 P(1724) has 7^4
 P(1785) has 8^4
funny how many have blocks of 4 eights...

So what is the smallest pandigital partition number?
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