IMO 1970 LL SWE49

For n \inN, let f(n) be the number of positive integers k \leqn

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IMO 1970 LL SWE49

Origin: SWE

Problem

For n \inN, let f(n) be the number of positive integers k \leqn that do not contain the digit 9. Does there exist a positive real number p such that f(n) n \geqp for all positive integers n?