what does J operator #: do?

What does the dyadic J operator #: do? I find its behavior puzzling

in light of its behavior as a monadic operator.

As a monadic operator, #: gives the base two expansion of its positive

integer argument.

#: i. 8

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

The operator #. is the left inverse of #:

#. #: i. 8

0 1 2 3 4 5 6 7

Furthermore, the dyadic version of #. behaves as follows:

given a positive integer m and the list of positive integers a,

m #. a gives the decimal value of the a considered as an integer base m.

5 #. 1 3 2

42

This leads me to expect m #: n to be the expansion in base m of the

decimal integer n. This is not the case. Is there an easy way to

get the expansion base m of n? Perhaps I don't quite get the picture

and am missing the obvious?