Record-Setters in the Stern Sequence

2022/05/12 by Keramatipour, Ali, Shallit, Jeffrey
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2205.06223

Abstract

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

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