A well-behaved cousin of the Hofstadter sequence
type: Item
instance of: scholarly article
title: A well-behaved cousin of the Hofstadter sequence
zbMATH Open document ID: 0766.11008
DOI: 10.1016/0012-365X(92)90145-6
author: Stephen M. Tanny
published in: Discrete Mathematics
publication date: 1993-01-16T00:00:00Z
review text: Let \(T(n)\) be a sequence of integers, defined by the recursion \(T(n)=T(n- 1-T(n-1))+T(n-2-T(n-2))\) for \(n>2\) with \(T(0)=T(1)=T(2)=1\). The treatment of the sequences similar than this is hard in general, as we know very little about them. So the results about the sequence \(T(n)\) obtained in the present paper are very interesting. Among others the author proves that \(T(n+1)=T(n)\) or \(T(n)+1\) for any \(n>0\); there are exactly \(x+2\) consecutive integers \(n\) for which \(T(n)=2^ x\); furthermore \(T(n)/n\to 1/2\) as \(n\to\infty\).
reviewed by: Péter Kiss
Mathematics Subject Classification ID: 11B37
zbMATH DE Number: 94360
zbMATH Keywords: Hofstadter sequence
zbMATH Keywords: recursive sequence of integers
MaRDI profile type: Publication
cites work: Q3872528
cites work: Q4792066
cites work: Conway's Challenge Sequence
cites work: Q4692934
description: scientific article; zbMATH DE number 94360