Regularity versus complexity in the binary representation of 3^n

Details Regularity versus complexity in the binary representation of 3^n Regularity versus complexity in the binary representation of 3^n

2009-02-18

arxiv.org/abs/0902.3257v2

Complex Systems 18 (2009) 367-377

Mathematics

Number Theory

10 pages, 7 figures; published version

Scientific paper

We use the grid consisting of bits of 3^n to motivate the definition of 2-adic numbers. Specifically, 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 regularity 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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