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prime hammock graph

It's a plot of the following:

Let $$f_{(n)} = \frac{np_n}{(p_1 + \ldots + p_n)}$$ so that $$g_{(n)} = \left|\space f_{(n)} - f_{(n-k)}\right| $$ where $n > k$ and $k = 5$ in this example.

For each $k$ the graph shows this 'hammock'-like pattern and it seems that the bigger the number is for $k$, the more the hammock unravels. I've never seen this kind of graph before and wondered if anyone recognizes it from some other function.

Marijn
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    Note: The OP has posted a variant of this question (with $k=1$) at http://math.stackexchange.com/questions/1415909/tau-and-grouping-of-prime-numbers – Barry Cipra Aug 31 '15 at 15:39

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