[seqfan] Variant Binary Representation and A068156

Dale Gerdemann dale.gerdemann at gmail.com
Thu Apr 16 00:56:01 CEST 2015

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?


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