  Let $P$ and $Q$ be two points on an elliptic curve defined over a number
field $K$. For $\alpha\in \text{End}(E)$, define $B_\alpha$ to be the
$\mathcal{O}_K$-integral ideal generated by the denominator of
$x(\alpha(P)+Q)$. Let $\mathcal{O}$ be a subring of $\text{End}(E)$, that is a
Dedekind domain. We will study the sequence $\{B_\alpha\}_{\alpha\in
\mathcal{O}}$. We will show that, for all but finitely many $\alpha\in
\mathcal{O}$, the ideal $B_\alpha$ has a primitive divisor when $P$ is a
non-torsion point and there exist two endomorphisms $g\neq 0$ and $f$ so that
$f(P)=g(Q)$. This is a generalization of previous results on elliptic
divisibility sequences.
