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Finding smallest sequence with no prime difference

Source: Abelkonkurransen Finale 2024, Problem 2a

March 8, 2024
algebraalgebra proposedSequence

Problem Statement

Positive integers a0<a1<⋯<ana_0<a_1<\dots<a_n, are to be chosen so that aj−aia_j-a_i is not a prime for any i,ji,j with 0≤i<j≤n0 \le i <j \le n. For each n≥1n \ge 1, determine the smallest possible value of ana_n.
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