  In this paper we discuss some relations between zeros of Lucas-Lehmer
polynomials and Gray code. We study nested square roots of 2 applying a "binary
code" that associates bits $0$ and $1$ to $\oplus$ and $\ominus$ signs in the
nested form. This gives the possibility to obtain an ordering for the zeros of
Lucas-Lehmer polynomials, which assume the form of nested square roots of 2.

Number Theory