RS-SMO 2014 Problem 4

We call natural number $n$ $crazy$ iff there exist natural numbers $a$ , $b >1$ such that $n=a^b+b$ . Whether there exist $2014$ consecutive natural numbers among which are $2012$ $crazy$ numbers?

Proposed by Milos Milosavljevic

Dataset text AI-MO AoPS. Quoted with source.

Official text: Serbian Mathematical Olympiad 2014 official paper, page 2.

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