  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.
