The following examples give evidence to the following conjecture contained in my paper [2]. All the main theoretical results can be found in that paper. Conjecture 1. Let d be a positive integer and ~s ∈ N. Then the set J(~s|p) is finite for every prime p. Example 2. The first example we would like to do is about the partial sums of ζ(2) series. The prime p = 7 is a little different from the ot...