Name
Abstract | ||
|---|---|---|
We consider representing natural numbers by expressions using only 1’s, addition, multiplication and parentheses. Let ( left| n right| ) denote the minimum number of 1’s in the expressions representing (n). The logarithmic complexity ( left| n right| _{log } ) is defined to be ({ 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 somewhere in the segment?, etc.). We establish a connection between this problem and another difficult problem: the seemingly “almost random” behaviour of digits in the base-3 representation of the numbers (2^n). |
Year | Venue | Field |
|---|---|---|
2015 | DCFS | Integer,Discrete mathematics,Combinatorics,Arithmetic function,Natural number,Algebra,Expression (mathematics),Cunningham chain,Experimental mathematics,Multiplication,Extremely hard,Mathematics |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
0 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Juris Cernenoks | 1 | 0 | 0.34 |
| Janis Iraids | 2 | 18 | 6.14 |
| Martins Opmanis | 3 | 30 | 3.84 |
| Rihards Opmanis | 4 | 0 | 1.01 |
| Karlis Podnieks | 5 | 53 | 6.64 |