Problem
TxO Math Bowl 2024 - Individuals B - Problem 11
The silver ratio \varepsilon is defined as \varepsilon = \sqrt{2} + 1. Consider the sequence
a_n = \left\lfloor \varepsilon^n - \frac{1}{(-\varepsilon)^n} \right\rfloor
for all positive integers n. What is the sum of the first 3 terms in the sequence that are prime?
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