Intervals of N-Exapansions With Many Gaps
| Authors | |
|---|---|
| Publication date | 2026 |
| Journal | Integers |
| Article number | A75 |
| Volume | Issue number | 26 |
| Number of pages | 33 |
| Organisations |
|
| Abstract | In this paper the number of gaps G(N,α) in N-expansions is investigated for values of α such that α is smaller but very close to the maximum value αmax = √N −1. As αdecreases from this maximum value, there is a large volatility of G. It is shown that for some N and α, the maximum value of G(N,α) may be more than 6 times as large as G(N,√N − 1). A method for determining the maximum value of G for all N ≥ 33 and α smaller than but very close to √N −1 is presented, and the maximum value of G for all N up to N = 5252, and α smaller than but very close to √N −1, is given explicitly. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.5281/zenodo.20597631 |
| Published at | https://math.colgate.edu/~integers/aa75/aa75.pdf |
| Other links | https://math.colgate.edu/~integers/vol26.html |
| Downloads |
aa75
(Final published version)
|
| Permalink to this page | |