# What does it mean if a sequence is indexed beyond its bounds?

I'm looking at a paper (On Base and Turyn Sequences by C. Koukouvinos, S. Kounias and K. Sotirakoglou) that describes an algorithm for finding specific sequences. Part of the algorithm involves finding an intermediary sequence $k$ of length $m$, $m < n$, where $n + 1$ is the length of the final sequence, and summing elements $k_1$ and $k_{n+1}$ then checking congruence. The problem is that $k$ is shorter than $n + 1$ (in some cases, much shorter). I don't think it's a typo in the paper ((33) on page 831 if you're curious), and from experimenting I don't think $n+1$ % $m$ is correct. Does anyone know what this means?

Thanks!

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Well, I am not sure I am looking at the correct page, but from what I see, $k$ seems to carry a double index everywhere, e.g., $k_{im}$. Added: Is it possible for you to also mention the page number (between 825-837) given in the document? –  Srivatsan Aug 31 '11 at 14:03
It's on page 831 - I've edited my post to add this. The m in the double index indicates which of the intermediary sequences this is - I left it out of my description to simplify things. The n+1 only appears in the first index, so the second index didn't seem important. –  Joel Aug 31 '11 at 14:08
Well, there's no standard meaning to indexing beyond the bound, if that's your question. It could mean something in this paper, but I presume the author would've indicated it somewhere. I am not brave enough to dig deeper :-) –  Srivatsan Aug 31 '11 at 14:12
That's okay, I don't blame you :-) As far as I can tell, they don't explain it in the paper. I was hoping there was some common convention for this... –  Joel Aug 31 '11 at 14:15