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each pos. integer exactly once in |a_1- a_2|,|a_2 - a_3|, ...,|a_k- a_{k+1}|,...

Source: 2013 Saudi Arabia IMO TST II p4

July 23, 2020
Sequencealgebranumber theory

Problem Statement

Determine if there exists an infinite sequence of positive integers a1,a2,a3,...a_1,a_2, a_3, ... such that (i) each positive integer occurs exactly once in the sequence, and (ii) each positive integer occurs exactly once in the sequence ∣a1−a2∣,∣a2−a3∣,...,∣a+k−ak+1∣,... |a_1 - a_2|, |a_2 - a_3|, ..., |a+k - a_{k+1}|, ...
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