
تعداد نشریات | 43 |
تعداد شمارهها | 1,685 |
تعداد مقالات | 13,849 |
تعداد مشاهده مقاله | 32,844,638 |
تعداد دریافت فایل اصل مقاله | 12,985,039 |
On twin EP numbers | ||
Transactions on Combinatorics | ||
مقاله 5، دوره 14، شماره 4، اسفند 2025، صفحه 261-270 اصل مقاله (1.85 M) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2024.138412.2092 | ||
نویسندگان | ||
Ömer Eğecioğlu* 1؛ Bünyamin Şahin2 | ||
1Department of Computer Science, University of California Santa Barbara, CA 93106, USA | ||
2Department of Mathematics, Faculty of Science, Selçuk University, Konya 42130, Turkey | ||
چکیده | ||
EP numbers were introduced by Estrada and Pogliani in 2008. These are positive integers $E(n)$ defined as the product of $n$ and the sum of the digits of $n$. Estrada and Pogliani suspected that there may be infinitely many twin EP numbers; i.e. those pairs in this sequence that differ by one. It is relatively easy to show that three consecutive EP numbers do not exist, and that no pair $E(n)$ and $E(m)$ can be twins for infinitely many bases $b$. The main contribution of our work is the result that indeed there are infinitely many twin EP numbers over any base. The proof is constructive and makes use of elementary properties of natural numbers. The forms of the twin EP numbers presented are derived from continued fractions. The behavior of the series of the reciprocals of twin EP numbers is also considered. | ||
کلیدواژهها | ||
EP number؛ twin EP number؛ continued fractions؛ reciprocal series | ||
مراجع | ||
[1] F. T. Adams-Watters and F. Ruskey, Generating functions for the digital sum and other digit counting sequences, J. Integer Seq., 12 (2009). | ||
آمار تعداد مشاهده مقاله: 285 تعداد دریافت فایل اصل مقاله: 225 |