Integer Complexity: Experimental and Analytical Results II

@inproceedings{Cernenoks2014IntegerCE,
  title={Integer Complexity: Experimental and Analytical Results II},
  author={Juris Cernenoks and Janis Iraids and Martins Opmanis and Rihards Opmanis and Karlis Podnieks},
  booktitle={Workshop on Descriptional Complexity of Formal Systems},
  year={2014}
}
We consider representing of natural numbers by expressions using 1's, addition, multiplication and parentheses. $\left\| n \right\|$ denotes the minimum number of 1's in the expressions representing $n$. The logarithmic complexity $\left\| n \right\|_{\log}$ is defined as $\left\| n \right\|/{\log_3 n}$. The values of $\left\| n \right\|_{\log}$ are located in the segment $[3, 4.755]$, but almost nothing is known with certainty about the structure of this "spectrum" (are the values dense… 

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