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NT sequence existence

Source: Mongolia 1999 Grade 10 P3

May 5, 2021

number theorySequences

Problem Statement

Does there exist a sequence

(a_n)_{n\in\mathbb N}

of distinct positive integers such that:
(i)

a_n<1999n

for all

n

; (ii) none of the

a_n

contains three decimal digits

1

?

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