Below are multiple sequences of letters. Both sequences can run infinitely, but for brevity's sake, I have only gone to 7 letters.
Both sequences are not continuations of one another, but they do share a relation. What is the third sequence of 7 letters? (The weird formatting is to make it easier, it serves no purpose. Capital I is a bit thinner than the other letters, so this way the pattern becomes clearer. Don't worry about them, just focus on the letters.)
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There is a hint in the title: it is an ODD sequence. The first thing to notice is that the first sequence is the first letters of all the odd numbers. The second is harder to determine, but still thinking of ODD numbers, you can determine that the second sequence is the second letters of all the odd numbers. Arranging it in a table and adding in extra information:
We begin to see a rather odd sequence indeed. Thus, the answer is E R V V N E I.