# A Unique Function

Algebra Level 4

For non-negative integers $a_1, a_2, a_3, \ldots , a_n \leq 9$, let

$f(a_1, a_2, \ldots , a_n) = a_1 + 11a_2 + 111a_3 + \ldots + \underbrace{111 \ldots 111}_{\text{Number of 1s}=n}a_n$

Find number of positive integers $N \lt 10^7$ such that there exists no possible set of non-negative integers $a_1, a_2, a_3, \ldots , a_n \leq 9$ such that $N = f(a_1, a_2, \ldots , a_n)$.

All of my problems are original.

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