Oregon State West Hall Dorm Math Series

solution.txt

At Oregon State University, when you walk into West Hall, there is a series of numbers written on 
the walls, near the ceiling.

The numbers are: 
3 7 31 127 [EXIT sign] 8191 131071 524287 8388607 536870911 2147483647 137438953471 2199023255551 
8796093022207 140737488355327 9007199254740991 576460752303423487 2305843009213693951

There is nothing else describing the numbers.  I wondered what they were & figured it out below.

----- SPOILERS BELOW -----

Below is a program that produces the following output:
2 3
3 7
5 31
7 127
11 2047  [indeed the EXIT sign covers something]
13 8191
17 131071
19 524287
23 8388607
29 536870911
31 2147483647
37 137438953471
41 2199023255551
43 8796093022207
47 140737488355327
53 9007199254740991
59 576460752303423487
61 2305843009213693951

So, the series is 2^p - 1 where p are the primes.

I checked via this Python code:
>>> for p in [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61]:
...   print(p,(2**p)-1)
...