Regularity Versus Complexity in the Binary Representation of 3^n
Author:
- Eric S. Rowland, October 31, 2009
Content:
We use the grid consisting of bits of 3^n to motivate the definition of 2-adic numbers. Specially, we exhibit diagonal stripes in the bits of 3^(2^n), which turn out to be the first in an infinite sequence of such structures. Our observations are explained by a 2-adic power series, providing some redularity among the disorder in the bits of powers of 3. Generally, the base-p representation of k^(p^n) has these features.
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