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Problem of the Week 908

Negabinary Numbers

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Find an algorithm for writing any positive integer in negabinary, i.e., as a sum of powers of -2.

For example,

 7 = 11011 = (-2)4 + (-2)3 + (-2)1 + (-2)0
19 = 10111 = (-2)4 + (-2)2 + (-2)1 + (-2)0
Source: This was a "contest problem" at a recent Mathematica conference. It was communicated to us by Stan Wagon.
© Copyright 2000 Stan Wagon. Reproduced with permission.

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14 March 2000 (Pi day: 3/14)