This analysis reveals optimal sets of θ using greedy two-term underapproximation methods with Fibonacci and Lucas sequences.
This paper studies the greedy two-term underapproximation of θ∈(0,1] using reciprocals of numbers from a Fibonacci-type sequence (cn)n=1∞. We find the set of θ whose greedy two-term underapproximation is the best among all two-term underapproximations using 1/cn's. We then derive a neat description of the set when (cn)n=1∞ is the Fibonacci sequence or the Lucas sequence.
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Mark Shiliaev (2025) studied this question.
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