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Interesting sequence

Source: Tuymaada 2015, Day 1, Problem 6, Junior League

July 10, 2017
number theory

Problem Statement

Is there sequence (an)(a_n) of natural numbers, such that differences {an+1−an}\{a_{n+1}-a_n\} take every natural value and only one time and differences {an+2−an}\{a_{n+2}-a_n\} take every natural value greater 20152015 and only one time ?
A. Golovanov
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