Venkatachala on the one hand, and Avdispahi\'c & Zejnulahi on the other, both studiied integer sequences with an unusual sum property defined in a greedy way, and proved many results about them. However, their proofs were rather lengthy and required numerous cases. In this paper, I provide a different approach, via finite automata, that can prove the same results (and more) in a simple, unified way. Instead of case analysis, we use a decision procedure implemented in the free software Walnut. Using these ideas, we can prove a conjecture of Quet and find connections between Quet's sequence and the "married" functions of Hofstadter.

翻译：一方面，Venkatachala，另一方面，Avdispahi\'c 与 Zejnulahi，均研究了具有奇特求和性质的贪婪定义整数序列，并证明了关于它们的诸多结论。然而，他们的证明相当冗长且需分析大量情形。本文提供一种基于有限自动机的不同方法，能够以简单统一的方式证明相同结论（甚至更多）。无需分情况讨论，我们使用自由软件Walnut中实现的决策过程。借助这些思想，我们证明了Quet的一个猜想，并揭示了Quet序列与Hofstadter“婚姻”函数之间的联系。