# A short note on integer complexity

@article{Steinerberger2014ASN, title={A short note on integer complexity}, author={Stefan Steinerberger}, journal={Contributions Discret. Math.}, year={2014}, volume={9} }

Building on an earlier approach by Isbell and Guy, this short note gives a new, constructive upper bound on the smallest number of 1's needed in conjunction with arbitrarily many +, *, and parentheses to write an integer n for generic integers n.

## 4 Citations

### An Application of Markov Chain Analysis to Integer Complexity

- Computer Science, Mathematics
- 2015

Markov chain methods are used to analyze a large class of algorithms, including one found by David Bevan that improves the upper bound to f(n) \leq 3.52 \log_{3}{n}$$ on a set of logarithmic density one.

### On Algorithms to Calculate Integer Complexity

- Mathematics, Computer ScienceIntegers
- 2019

A method is discussed that provides a strong uniform bound on the number of summands that must be calculated for almost all $n$ and potential improvements to this algorithm are discussed.

### Algorithms for determining integer complexity

- Computer Science
- 2014

Three algorithms to compute the complexity of all natural numbers, each superior to the one in [11], are presented and it is shown that they run in time $O(N^\alpha)$ and space $N\log\log N)$.

### Integer Complexity: Experimental and Analytical Results II

- MathematicsDCFS
- 2015

This work considers representing of natural numbers by expressions using 1's, addition, multiplication and parentheses, and the so-called $P$-algorithms - a family of "deterministic" algorithms for building representations of numbers.

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