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Is it possible to mathematically deduce the next element (to the right) in the following series? It continues in the same pattern to the left ($n-1$ copies of the positive integer $n$ on the left).
$$ \ldots, 7,6,6,6,6,6,5,5,5,5,4,4,4,3,3,2,?$$

Is there a most natural continuation (analytical or smooth or nice) possibly of several or infinite elements?

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    Do you have an extra "6"?2011-12-05
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    Yes, fixed thasnk2011-12-05
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    If you have a simpler description (in English!) in mind, please add that as well. Do you want the sequence to contain $n$ copies of every positive integer $n$?2011-12-05
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    Your definition doesn't allow for any natural next element - you have defined a sequence that termintes on the right.2011-12-05
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    Maybe OP means, 2,3,3,4,4,4,...? n-1 copies of n?2011-12-05
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    "Analytic" and "smooth" don't make sense for integer sequences. Sequences don't have unique next elements.2011-12-05
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    From the online encyclopedia of integer sequences: http://oeis.org/A0030572011-12-05
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    So if you're looking for a formula, try $\lceil \frac{1}{2} (\sqrt{1+8n}+1) \rceil$.2011-12-05

2 Answers 2