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a_n=a_{a_{n-1}}+a_{a_{n+1}}, of positive integers

Source: 2014 Belarus TST 5.2

December 29, 2020
Sequencerecurrence relationalgebranumber theory with sequences

Problem Statement

Find all sequences (an)(a_n) of positive integers satisfying the equality an=aan−1+aan+1a_n=a_{a_{n-1}}+a_{a_{n+1}} a) for all n≥2n\ge 2 b) for all n≥3n \ge 3
(I. Gorodnin)
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