MathDB

3

Part of 2019 Bulgaria National Olympiad

Problems(1)

A sequence of integers

Source: Bulgaria National Olympiad 2019

4/20/2019
Find all real numbers a,a, which satisfy the following condition:
For every sequence a1,a2,a3,…a_1,a_2,a_3,\ldots of pairwise different positive integers, for which the inequality an≤ana_n\leq an holds for every positive integer n,n, there exist infinitely many numbers in the sequence with sum of their digits in base 4038,4038, which is not divisible by 2019.2019.
Integer sequenceinequalities