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Let [unparseable or potentially dangerous latex formula] be an odd prime. The sequence [unparseable or potentially dangerous latex formula] is defined as follows: [unparseable or potentially dangerous latex formula] and, for all [unparseable or potentially dangerous latex formula] is the least positive integer that does not form an arithmetic sequence of length [unparseable or potentially dangerous latex formula] with any of the preceding terms. Prove that, for all [unparseable or potentially dangerous latex formula] is the number obtained by writing [unparseable or potentially dangerous latex formula] in base [unparseable or potentially dangerous latex formula] and reading the result in base [unparseable or potentially dangerous latex formula] .