MathDB

x formed by digits of the sequence is rational

Source: Romanian TST 2002

February 5, 2011

number theory proposednumber theory

Problem Statement

Let

(a_n)_{n\ge 1}

be a sequence of positive integers defined as

a_1,a_2>0

and

a_{n+1}

is the least prime divisor of

a_{n-1}+a_{n}

, for all

n\ge 2

.
Prove that a real number

x

whose decimals are digits of the numbers

a_1,a_2,\ldots a_n,\ldots

written in order, is a rational number.
Laurentiu Panaitopol