  We consider a scenario where spatially separated observers share a genuinely
multiparty entangled quantum state with each local observer possessing a single
qubit. A particular qubit is acted upon by sequential and independent
observers. We study the recycled detection of genuine multipartite entanglement
of multiqubit states by any one of the sequential observers and the rest of the
spatially separated parties. We show that for it is possible to sequentially
detect genuine multiparty entanglement, arbitrarily many times for an
arbitrarily large number of parties. Modified genuine multiparty entanglement
witness operators for unsharp measurements by sequential observers are deduced,
which are then employed to show that an arbitrary number of observers can
sequentially detect genuine multisite entanglement of
Greenberger-Horne-Zeilinger and cluster states of an arbitrary number of
parties. Extensions to multiparty generalized Greenberger-Horne-Zeilinger
states and a class of mixed states are also shown to be achievable.
