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Digits of pi: limits to the seeming randomness II
Paula Nataniela Roba, Karlis Podnieks
According to a popular belief, the decimal digits of mathematical constants such as π behave like statistically independent random variables, each taking the values 0, 1, 2, 3, 4,…
Digits of pi: limits to the seeming randomness
Karlis Podnieks
The decimal digits of are widely believed to behave like as statistically independent random variables taking the values , with equal probabiliti…
Integer Complexity: Experimental and Analytical Results II
Juris Čerņenoks, Jānis Iraids, Mārtiņš Opmanis +2
We consider representing of natural numbers by expressions using 1's, addition, multiplication and parentheses. denotes the minimum number of 1's in the expres…
Integer Complexity: Experimental and Analytical Results
Jānis Iraids, Kaspars Balodis, Juris Čerņenoks +3
We consider representing of natural numbers by arithmetical expressions using ones, addition, multiplication and parentheses. The (integer) complexity of n -- denoted by ||n|| -- i…