MathDB
Tricky Sequence

Source: Korean National Olympiad P5

November 24, 2020
combinatoricsInteger sequence

Problem Statement

For some positive integer nn, there exists nn different positive integers a1,a2,...,ana_1, a_2, ..., a_n such that (1)(1) a1=1,an=2000a_1=1, a_n=2000 (2)(2) ∀i∈Z\forall i\in \mathbb{Z} s.t.s.t. 2≤i≤n,ai−ai−1∈{−3,5}2\le i\le n, a_i -a_{i-1}\in \{-3,5\} Determine the maximum value of n.
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