Integer Complexity and Mixed Binary-Ternary Representation
K Amano - 33rd International Symposium on Algorithms and …, 2022 - drops.dagstuhl.de
The integer complexity of a natural number n, denoted by‖ n‖, is the smallest number of
1's needed to express n using an arbitrary combination of addition and multiplication (and …
1's needed to express n using an arbitrary combination of addition and multiplication (and …
An application of markov chain analysis to integer complexity
CE Shriver - arXiv preprint arXiv:1511.07842, 2015 - arxiv.org
The complexity $ f (n) $ of an integer was introduced in 1953 by Mahler & Popken: it is
defined as the smallest number of $1 $'s needed in conjunction with arbitrarily many+,* and …
defined as the smallest number of $1 $'s needed in conjunction with arbitrarily many+,* and …
[PDF][PDF] Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada jmaxwellcampbell@ gmail. com
JM Campbell - INTEGERS, 2024 - math.colgate.edu
Abstract The (Mahler–Popken) complexity∥ n∥ of a natural number n is the smallest
number of ones that can be used via combinations of multiplication and addition to express …
number of ones that can be used via combinations of multiplication and addition to express …
Digits of pi: limits to the seeming randomness
K Podnieks - arXiv preprint arXiv:1411.3911, 2014 - arxiv.org
The decimal digits of $\pi $ are widely believed to behave like as statistically independent
random variables taking the values $0, 1, 2, 3, 4, 5$, $6, 7, 8, 9$ with equal probabilities …
random variables taking the values $0, 1, 2, 3, 4, 5$, $6, 7, 8, 9$ with equal probabilities …
Some Conceptual and Measurement Aspects of Complexity, Chaos, and Randomness from Mathematical Point of View
F Öztürk - Chaos, Complexity and Leadership 2018: Explorations …, 2020 - Springer
One of the main purposes of the mankind is to understand and explain the dynamics of real-
world phenomena, ie, modeling them, and also to build predictive models for their …
world phenomena, ie, modeling them, and also to build predictive models for their …
Some Conceptual and Measurement Aspects of Complexity, Chaos, and Randomness from Mathematical
F Öztürk - Chaos, Complexity and Leadership 2018: Explorations …, 2020 - books.google.com
One of the main purposes of the mankind is to understand and explain the dynamics of real-
world phenomena, ie, modeling them, and also to build predictive models for their …
world phenomena, ie, modeling them, and also to build predictive models for their …