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Record-Setters in the Stern Sequence
- Publication Year :
- 2022
-
Abstract
- Stern's diatomic series, denoted by $(a(n))_{n \geq 0}$, is defined by the recurrence relations $a(2n) = a(n)$ and $a(2n + 1) = a(n) + a(n + 1)$ for $n \geq 1$, and initial values $a(0) = 0$ and $a(1) = 1$. A record-setter for a sequence $(s(n))_{n \geq 0}$ is an index $v$ such that $s(i) < s(v)$ holds for all $i < v$. In this paper, we give a complete description of the record-setters for the Stern sequence.
- Subjects :
- Mathematics - Combinatorics
Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2205.06223
- Document Type :
- Working Paper