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arXiv · 2411.19364

The 2-complexity of even positive integers

Pengcheng Zhang
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Abstract

The question of integer complexity asks about the minimal number of $1$'s that are needed to express a positive integer using only addition and multiplication (and parentheses). In this paper, we propose the notion of $l$-complexity of multiples of $l$, which specializes to integer complexity when $l=1$, prove several elementary results on $2$-complexity of even positive integers, and raise some interesting questions on $2$-complexity and in general $l$-complexity.

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Pengcheng Zhang. 2024-11-28. The 2-complexity of even positive integers. https://doi.org/10.5281/zenodo.14340011

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