Record-Setters in the Stern Sequence

Abstract

Stern's diatomic series, denoted by $(a(n){)}_{n\ge 0}$, is defined by the recurrence relations $a(2n)=a(n)$ and $a(2n+1)=a(n)+a(n+1)$ for $n\ge 1$, and initial values $a(0)=0$ and $a(1)=1$. A record-setter for a sequence $(s(n){)}_{n\ge 0}$ 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.