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Unusual binary representation (Posted on 2005-06-14) Difficulty: 3 of 5
Show that every positive integer is an alternating sum of strictly increasing powers of 2.

For example, 5=2^0 -2^2 +2^3 and 8=-2^3 +2^4 are alternating sums of strictly increasing powers of 2 (8=2^3 is ok too).

10=-2^1 -2^2 +2^4 is a strictly increasing sum but not alternating.

4=2^1 -2^1 +2^2 is alternating but not strictly increasing.

(author: prof Dan Shapiro of Ohio State University)

See The Solution Submitted by McWorter    
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Some Thoughts re: Negabinary | Comment 4 of 9 |
(In reply to Negabinary by Richard)

No, it's not the same. In negabinary, coefficients do not have to alternate.
  Posted by Old Original Oskar! on 2005-06-15 00:09:14

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