  A Friedman number is a positive integer which is the result of an expression
combining all of its own digits by use of the four basic operations,
exponentiation and digit concatenation. A "nice" Friedman number is a Friedman
number for which the expression constructing the number from its own digits can
be represented with the original order of the digits unchanged. One of the
fundamental questions regarding Friedman numbers, and particularly regarding
nice Friedman numbers, is how common they are among the integers. In this
paper, we prove that nice Friedman numbers have density 1, when considered in
binary, ternary or base four.
