MathDB

A sequence as in Euclid's proof, not containing certain primes

Source: Germany 2018, Problem 5

June 17, 2018

number theorySequencePrime factorprimes

Problem Statement

We define a sequence of positive integers

a_1,a_2,a_3,\dots

as follows: Let

a_1=1

and iteratively, for

k =2,3,\dots

let

a_k

be the largest prime factor of

1+a_1a_2\cdots a_{k-1}

. Show that the number

11

is not an element of this sequence.