K. $0 \times 10^{15}$

The title is an important hint. What is $0 \times 10^{15}$ . Of course you're going to say 0 but let's look a bit closer. Hmmm, we can certainly write it as 0E15. Wait a minute, that looks like OEIS. Simple google search (or I think most of you who did trollathon should know this by now) gives you the site oeis.com, home of integer sequences. Now, let's see. Input all those large numbers in each pair (with an A in front, that's what the code of oeis looks like). Find A007088, A000578, and A011557. Now, let's see. Conincidentally, the 9th term of A007088, 11th term of A000578 and 4th term of A011557 are all 1000! (not 1000 factorial :P) You might also notice that 1k actually denotes 1000, but anyway now we look at A007089. Numbers in base 3, starting with 0. Now, 1000 in base 3 is 27 in decimal base, so it's the 28th term of the sequence. Thus, the answer is $\boxed{28}$ !