Some arithmetic properties of certain sequences

Roettger, E.L. ; Williams, H.C.

Journal of integer sequences, Tome 18 (2015) no. 6

Résumé

In an earlier paper it was argued that two sequences, denoted by ${U_{n}}$ and ${W_{n}}$, constitute the sextic analogues of the well-known Lucas sequences ${u_{n}}$ and ${v_{n}}$. While a number of the properties of ${U_{n}}$ and ${W_{n}}$ were presented previously, several arithmetic properties of these sequences were only mentioned in passing. In this paper we discuss the derived sequences ${D_{n}}$ and ${E_{n}}$, where $D_{n} = gcd(W_{n} - 6 R^{n},U_{n})$ and $E_{n} = gcd(W_{n},U_{n})$, in greater detail and show that they possess many number-theoretic properties analogous to those of ${u_{n}}$ and ${v_{n}}$, respectively.

Détail

Classification : 11B37, 11Y11, 11B50
Keywords: linear recurrence, Lucas function, primality testing