Geodesic
Jumping sequences
Journal of integer sequences, Tome 11 (2008) no. 4
An integer sequence $a(n)$ is called a jump sequence if $a(1)=1$ and $1\leq a(n)$ for $n\geq 2$. Such a sequence has the property that $a^k(n)=a(a(\cdots(a(n))\cdots))$ goes to 1 in finitely many steps. We call the pattern $(n,a(n),a^2(n),\ldots,a^\ell(n)=1)$ a jumping pattern from $n$ down to 1. In this paper we look at jumping sequences that are weight minimizing with respect to various weight functions (where a weight $w(i,j)$ is given to each jump from $j$ down to $i$).
Classification : 11Y55, 11B99
Keywords: jumping sequences, sieving, pell numbers 
@article{JIS_2008__11_4_a6,
     author = {Butler,  Steve and Graham,  Ron and Zang,  Nan},
     title = {Jumping sequences},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {4},
     zbl = {1204.11186},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_4_a6/}
}
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Butler,  Steve; Graham,  Ron; Zang,  Nan. Jumping sequences. Journal of integer sequences, Tome 11 (2008) no. 4. http://geodesic.mathdoc.fr/item/JIS_2008__11_4_a6/