User blog comment:Deedlit11/Bignum Bakeoff appetizer/@comment-5529393-20140916042352/@comment-5529393-20140916044502

Based on Vell's code:

i = 9 ** 9 ** 9 b = 2

def B(n): j = 0 o = 1 while b*o <= n:		j += 1 o *= b	return (b+1)**B(j) + B(n - o) if n else 0

while i:	i = B(i) - 1 b += 1 print b

103 characters.