Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity versus complexity in the binary representation of 3^n   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.

30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat