Request for information about basis representation

[Andrew Plewe]

I'm looking for links, papers, etc. about the following topic.

Let's define S as the set of coefficients in the binary representation of some number n.  So, if n = 35, S = {1, 0, 0, 0, 1, 1}
because the binary representation is:

1(2^5) + 0(2^4) + 0(2^3) + 0(2^2) + 1(2^1) + 1(2^0) = 35

I'm interested in the algebraic properties of the set of numbers whose coefficients S are fixed but whose base varies from two to
infinity. In the case of 35, this set is {35, 247, 1029...}, or:

1(3^5) + 0(3^4) + 0(3^3) + 0(3^2) + 1(3^1) + 1(3^0) = 247

1(4^5) + 0(4^4) + 0(4^3) + 0(4^2) + 1(4^1) + 1(4^0) = 1029


I have George Andrew's book "Number Theory" at home and I'll work on it myself if nothing else is out there, however if someone else
has specifically studied the properties of this type of set I'd like to see their work.  Any help is appreciated -- thanks!

	-Andrew Plewe-