On min-base palindromic representations of powers of 2

A positive integer N is palindromic in the base b when N = ∑_i=0^k c_i b^i, c_k≠ 0,and c_i=c_k-i, i=0,1,2,...,k, Focusing on powers of 2, we investigate the smallest base b when N=2^n is palindromic in the base b.