> 0 to 127. 127 is a power of 2 minus 1, which should be a hint; in specific, it's two to the seventh minus one ...

To expand on this a tiny bit, a power of two minus one is called a "Mersenne number". If the number is prime, it's called ... wait for it ... a Mersenne prime.

When expressed in binary, Mersenne numbers are an uninterrupted series of one digits: 11111... of varying lengths.

http://mathworld.wolfram.com/MersenneNumber.html