[seqfan] Variant Binary Representation and A068156

[Dale Gerdemann]

In normal binary, the 1's represent powers of 2 and the 0's are just place
holders. Suppose, in the interest of fairness and political correctness, it
has been decided that the 1's and 0's should play equal roles. So a 1 with
n 0's to the left represents 2^n and likewise, a 0 with n 1's to the left
also represents 2^n.

Now the question: given an equal number of 1's and 0's, what is the
smallest number that you can construct? I get the  answer A068156. Any
thoughts on why this might be true?

Dale