Jumping sequences
| dc.creator | Butler, Steve | |
| dc.creator | Graham, Ron | |
| dc.creator | Zang, Nan | |
| dc.date | 2008-07-18 | |
| dc.date.accessioned | 2026-07-07T09:51:16Z | |
| dc.date.available | 2026-07-07T09:51:16Z | |
| dc.description | An integer sequence a(n) is called a jump sequence if a(1)=1 and 1<=a(n)<n for n>=2. Such a sequence has the property that a^k(n)=a(a(...(a(n))...)) goes to 1 in finitely many steps and we call the pattern (n,a(n),a^2(n),...,a^k(n)=1) a jumping pattern from n down to 1. In this paper we look at jumping sequences which are weight minimizing with respect to various weight functions (where a weight w(i,j) is given to each jump from j down to i). Our main result is to show that if w(i,j)=(i+j)/i^2 then the cost minimizing jump sequence has the property that the number m satisfies m=a^q(p) for arbitrary q and some p (depending on q) if and only if m is a Pell number. | |
| dc.description | 13 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0807.2890 | |
| dc.identifier | http://arxiv.org/abs/0807.2890 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165228 | |
| dc.subject | Combinatorics | |
| dc.subject | 11Y55; 11B99 | |
| dc.title | Jumping sequences | |
| dc.type | text |