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Posts Tagged ‘pairing functions’
Where are the powers of two?
June 29, 2011
2 comments
The following construction gives an interesting pairing map between the positive integers and the lattice of integer-valued points in the plane:
- Place
at the origin.
- For each level
populate the
points of the plane on the square with vertices
starting from
at the position
and going counter-clockwise.
After pairing enough positive integers on the lattice, pay attention to the powers of two: they all seem to be located on the same two horizontal lines: 
Is this statement true?
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