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As I’ve previously mentioned, Leo loves large numbers. While we were looking at factorials with huge numbers of digits in the result — a favorite puzzle being predicting the number of trailing zeros — he noticed that there were a few digits of Pi embedded in one of them. So we wrote a program to find the largest run of Pi embedded in a factorial…or at least as far as we felt like letting the program run, which was up to 26000!

Here’s the log:

Pi digs  n(!)
1          8
2         32
3         35
4        116
5        147
6        380
7       3057
8       5599
9      14192

That’s it under 26000! I’ll spare you the 52765 digits of 14192! Suffice it to say that the sequence “314159265″ shows up at the 48996-th digit!

(Before you complain, of course there are many occurrences of shorter sequences all over the place. This is just the location of the first occurrence of each next longest subsequence, so, for example, there are 3, and 31, and 314’s all over the place, but the first 314 occurs in 35!)

I’m not going to bother showing you the couple of line of simple Lisp code that it took to program this up. …Exercise for the reader!   🙂