dump and remove data from infinite growing arraylist in java

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I am looking out for an approach where I have an ArrayList that is kept on growing, and on a regular basis, I need to dump those data. Those dumped data should not repeat(which are already dumped, basically my aim is to remove them from the list).

eg. list = {1,2,3,4,5,6...........infinite} its continuous growing in one thread.

below are for another

on regular interval at time t1:

 Fetch all data from the list as of now then dump

on another interval at time t2:

Fetch all data from the list, except for data at t1, as of now then dump 

continue...

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