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Combinatorics Difficulty 5.0 AIME, harder Find the answer United Kingdom

Beads numbered 1 to $n$ , where $n > 1$ , are threaded onto a bracelet. What is the smallest value of $n$ for which this can be done in such a way that no two consecutive numbers are next to each other?

(A) $3$ (B) $4$ (C) $5$ (D) $6$ (E) $7$

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