2a

Part of 2024 Abelkonkurransen Finale

Problems(1)

Finding smallest sequence with no prime difference

Source: Abelkonkurransen Finale 2024, Problem 2a

Positive integers

a_0<a_1<\dots<a_n

, are to be chosen so that

a_j-a_i

is not a prime for any

i,j

0 \le i <j \le n

n \ge 1

, determine the smallest possible value of

a_n

algebraalgebra proposedSequence