The (k, l)-Göbel sequences defined by Ibstedt remain integers for the first (in some cases, many) terms, but for selected values of (k, l) computations show that the terms eventually stop being integers. It is still unresolved whether the integrality of these sequences breaks down for all k, l ≥ 2. In this article, we prove the non-integrality for a specific class of (k, l) values. Our proof is based on geometric arguments related to the distribution of quadratic residues modulo a prime.