MathDB

M2656

Part of Kvant 2021

Problems(1)

Sequence has finitely many composite numbers

Source: Kvant Magazine No. 6 2021 M2656

3/9/2023
The increasing sequence of natural numbers a1,a2,…a_1,a_2,\ldots is such that for every n>100n>100 the number ana_n is equal to the smallest natural number greater than an−1a_{n-1} and not divisible by any of the numbers a1,…,an−1a_1,\ldots,a_{n-1}. Prove that there is only a finite number of composite numbers in such a sequence.
Proposed by P. Kozhevnikov
number theoryKvant