  There is a well-known bijection between finite binary sequences and integer
partitions. Sequences of length r correspond to partitions of perimeter r+1.
Motivated by work on rational numbers in the Calkin-Wilf tree, we classify
partitions whose corresponding binary sequence is a palindrome. We give a
generating function that counts these partitions, and describe how to
efficiently generate all of them. Atypically for partitions generating
functions, we find an unusual significance to prime degrees. Specifically, we
prove there are nontrivial palindrome partitions of n except when n=3 or n+1 is
prime. We find an interesting new "branching diagram" for partitions, similar
to Young's lattice, with an action of the Klein four group corresponding to
natural operations on the binary sequences.
