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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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Negabinary | Comment 3 of 9 |

Prof. Shapiro seems to have reinvented "negabinary."

See 

Eric W. Weisstein. "Negabinary." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Negabinary.html

  Posted by Richard on 2005-06-14 21:54:24
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