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Find S_1024 for sequence of sets of natural numbers

Source: AIMO 2008, TST 5, P1, Suggested by Gunther Vogel

January 4, 2009
inductionLaTeXalgebra unsolvedalgebra

Problem Statement

A sequence (Sn),n≥1 (S_n), n \geq 1 of sets of natural numbers with S1={1},S2={2} S_1 = \{1\}, S_2 = \{2\} and Sn+1={k∈N∣k−1∈Sn XOR k∈Sn−1}.{ S_{n + 1} = \{k \in }\mathbb{N}|k - 1 \in S_n \text{ XOR } k \in S_{n - 1}\}. Determine S1024. S_{1024}.
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