  Let $K$ be an arbitrary field. Let $\a = (a_1< ... <a_n)$ be a sequence of
positive integers. Let $C(\a)$ be the affine monomial curve in ${\mathbb A}^n$
parametrized by $t\to (t^{a_1}, ..., t^{a_n})$. Let $I(\a)$ be the defining
ideal of $C(\a)$ in $K[x_1, ..., x_n]$. For each positive integer $j$, let
$\a+j$ be the sequence $(a_1 + j, ..., a_n+j)$. In this paper, we prove the
conjecture of Herzog and Srinivasan saying that the betti numbers of $I(\a +
j)$ are eventually periodic in $j$ with period $a_n -a_1$. When $j$ is large
enough, we describe the betti table for the closure of $C(\a+j)$ in $\PP^n$.
