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We consider Hamilton cycles in the random digraph $D_{n,m}$ where theorientation of edges follows a pattern other than the trivial orientation inwhich the edges are oriented in the same direction as we traverse the cycle. Weshow that if the orientation forms a periodic pattern, other than the trivialpattern, then approximately half the usual $n\log n$ edges are needed toguarantee the existence of such Hamilton cycles a.a.s.

On the existence of Hamilton cycles with a periodic pattern in a random digraph