In order to find the next element I consulted The on-line encyclopedia of integer sequences. Funnily enough they only have the sequence up to 82000. There is a reference to this paper where the author claims that the next number would be at least 10**21 according to his experiments.

In reply to Re^2: Can It Be Written In Base X With Only 1s And 0s by hdb
in thread Can It Be Written In Base X With Only 1s And 0s by Limbic~Region

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