تقرير
Elated Numbers
| العنوان: | Elated Numbers |
|---|---|
| المؤلفون: | Fox, N. Bradley, Fox, Nathan H., Grundman, Helen G., Lynn, Rachel, Namoijam, Changningphaabi, Vanderschoot, Mary |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11A63 |
| الوصف: | For a base $b \geq 2$, the $b$-elated function, $E_{2,b}$, maps a positive integer written in base $b$ to the product of its leading digit and the sum of the squares of its digits. A $b$-elated number is a positive integer that maps to $1$ under iteration of $E_{2,b}$. The height of a $b$-elated number is the number of iterations required to map it to $1$. We determine the fixed points and cycles of $E_{2,b}$ and prove a range of results concerning sequences of $b$-elated numbers and $b$-elated numbers of minimal heights. Although the $b$-elated function is closely related to the $b$-happy function, the behaviors of the two are notably different, as demonstrated by the results in this work. Comment: 21 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2409.09863 |
| رقم الأكسشن: | edsarx.2409.09863 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |