Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Several results on sequences which are similar to the positive integers   Sequence of positive integers $\{x_n\}_{n\geq1}$ is called similar to
$\mathbb {N}$ respectively a given property $A$ if for every $n\geq1$ the
numbers $x_n$ and $n$ are in the same class of equivalence respectively
$A\enskip(x_n\sim n (prop \enskip A).$ If $x_1=a(>1)\sim1 (prop\enskip A)$ and
$x_n>x_{n-1}$ with the condition that $x_n$ is the nearest to $x_{n-1}$ number
such that $x_n\sim n (prop \enskip A),$ then the sequence $\{x_n\}$ is called
minimal recursive with the first term $a\enskip(\{x_n^{(a)}\}).$ We study two
cases: $A=A_1$ is the value of exponent of the highest power of 2 dividing an
integer and $A=A_2$ is the parity of the number of ones in the binary expansion
of an integer. In the first case we prove that, for sufficiently large $n,
\enskip x_n^{(a)}=x_n^{(3)};$ in the second case we prove that, for $a>4$ and
sufficiently large $n,\enskip x_n^{(a)}=x_n^{(4)}.$

22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org