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I'm having difficulty explaining what I am after in this question. I was rather hoping that with anon's kind assistance, I had managed to clarify things a bit, but appparently not. I have looked at the help centre as advised, but don't really have any idea on how to proceed. My degree is not in maths, as you might have guessed, so I am struggling a bit on this one & would very much welcome any suggestions for improvement.

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    $\begingroup$ I'm not sure what the regularity of the oscillations you mention is. The sequence $a_k\cdot\mu - k$ is indeed periodic. For $n = 10$ its period is $5447823150$, so the plot for $k\leqslant 10^5$ can't reveal the periodicity, you'd need to plot for $k\leqslant 10^{10}$ or so to see it, but plotting $k$ on log-scale makes it less than obvious. Are you referring to a finer-grained regularity? $\endgroup$ Apr 14, 2015 at 12:39
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    $\begingroup$ @DanielFischer of course eventually all oscillations of this kind will become periodic, and you are absolutely right, I was referring to the regularity of oscillations on the way to uniform periodicy. This is a very helpful observation - thank you :) $\endgroup$
    – martin
    Apr 14, 2015 at 12:42
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    $\begingroup$ @DanielFischer If I were to reword the question to include this information, is there a chance the question might be reopened? $\endgroup$
    – martin
    Apr 14, 2015 at 12:49
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    $\begingroup$ Sure, it's closed as "unclear what you're asking", once it has been edited to make that sufficiently clear, it should be reopened. At the moment, it is in the reopen queue. Let's see what the reviewers think. But if you try to make it clearer before the review is finished, it probably wouldn't hurt. $\endgroup$ Apr 14, 2015 at 12:53
  • $\begingroup$ @DanielFischer many thanks :) $\endgroup$
    – martin
    Apr 14, 2015 at 13:54
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    $\begingroup$ I usually find that when I can frame something into a question others can answer I usually find the answer on my own $\endgroup$ Apr 15, 2015 at 2:27

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