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Dec 23, 2013 at 18:16 comment added The Masked Avenger This is becoming more interesting. Eventually, you can cut down on the number of candidates by looking at those multiples "on the edges" of large gaps between totients. You might try some numerical experiments for n=7 and 8.
Dec 23, 2013 at 18:07 comment added The Masked Avenger In spite of my suspicions, it seems clear that you want to look mod $P_n$ at the $\phi(P_{n-1})$ many multiples of $p_n$ to find your example. You may get some nice results from this if you can show one nontrivial such sequence exists.
Dec 23, 2013 at 17:55 history answered The Masked Avenger CC BY-SA 3.0