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detect subset in series

Dear R Users, I am curious whether there is any simple solution o my problem.

My example 'series':
series <- c(1,1,1,0,1,0,0,1,1,0,0,0,0,1)

My 'subset' of interest:
subset <- c(0,0,0,0)

Is there any function which tells me that the subset exists in my series,
and gives me position where in series is starts. In provided example the
subset exists and covers the elements 10:13 of the 'series'.

Thanks a lot , robert

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