## 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.