Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the shortest addition chain of numbers of special forms   In this paper we study the shortest addition chains of numbers of special
forms. We obtain the crude inequality $$\iota(2^n-1)\leq n+1+G(n)$$ for some
function $G:\mathbb{N}\longrightarrow \mathbb{N}$. In particular we obtain the
weaker inequality $$\iota(2^n-1)\leq n+1+\left \lfloor \frac{n-2}{2}\right
\rfloor$$ where $\iota(n)$ is the length of the shortest addition chain
producing $n$. Additionally, we prove an inequality relating the length of
addition chains producing number of the form $2^n-1$ to the length of their
shortest addition chain producing their exponents. In particular, we obtain the
inequality $$\delta(2^n-1)\leq n-1+\iota(n)+K(n)$$ where $\delta(n)$ and
$\iota(n)$ denotes the length of an addition chain and the shortest addition
chain producing $n$, respectively, with $K:\mathbb{N}\longrightarrow
\mathbb{R}$.

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc