MathDB

A sequence

a_0,a_1,a_2,\ldots ,a_n,\ldots

of positive integers is constructed as follows: [*]if the last digit of

a_n

is less than or equal to

5

then this digit is deleted and

a_{n+1}

is the number consisting of the remaining digits. (If

a_{n+1}

contains no digits the process stops.) [*]otherwise

a_{n+1}=9a_n

. Can one choose

a_0

so that an infinite sequence is obtained?

Problem Statement