Proof of Northshield's conjecture concerning an analogue of Stern's sequence for ℤ[√(2)]

2017/09/06 by Michael James Coons, Coons, Michael
Computer Science · Mathematics · #05A16 #11B37 #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1709.01987

openalex publication_date 2017/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a conjecture of Northshield by determining the maximal order of his analogue of Stern's sequence for ℤ[√(2)]. In particular, if b is Northshield's analogue, we prove that \limsup_n→∞\frac2b(n)(2n)^{log₃ (√(2)+1)}=1.

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