Some first data on growth of D in the multiplicative case

I’ve now put on the wiki a C++ program that allows to investigate the growth of D as a function of length for completely-multiplicative sequences, depending on how one chooses the values at prime indices.

Here is a first plot: for the first values I’ve imposed only x_1=+1,  and then chose to impose x_p=+1 or x_p=-1 depending on which gave the smallest quantity \ell_s(q), where q is the next prime and \ell_s(q):=\sum_{d=1}^q s_d(q) with s_d(q) the partial sum of the d-HAP up to q.

On the plot I’ve show f(x)=\log (x) (the very flat curve), the partial sums of the sequence and its first few HAPs, and both D(n) and -D(n).

For comments and analysis, please see the wiki.



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