## Emboding exquisite viewpoints that cut the domain of definition structured by the R-sequence

Take all the blockers from the set {3,10,30,104,312,1040,…} (from the B-sequence). Notice that each number from the R-sequence corresponds the prime number. Each set of n-blockers, e.g. {27,28,30} contains the first (and only odd) number of the form $3^k$, here: 27, and the last – by  the definition of the B-sequence.

Knowing that for every element of the set of n-blockers, e.g. {27,28,30}, there exist the same amount of primes, in this case 3 primes. The element of the corresponding primes for each n-blocker could be dependant on the difference between the biggest and smallest of blockers within the n-blocker. In this example, we’d have 30-27=3. For a 4-blocker, ie.. {81,84,88,90,100,104}, we’d have 104-81=23.

Lets now investigate this fuction defined as $F(n) = B(n) - 3^n$. Based on the character of  numbers, we might suspect that $3^n$ has its roots in binominal sum. We could also suspect something of this kind from B(n). However, starting with the most generic idea would be to take a closer look at its elements.

These elements are (starting from 2-blocker): {3, 23,  69, 311,..}. As I don’t have more elements of the R-sequence, thus B-sequence, therefore only this amount of values of the F function. The number of primes, if dependant of this as tested, then will be dependant on its cummulative measure, including two additional elements of 1-blocker, i.e. {2,3}. Thus, we have 2 (for 1-blocker {2,3}), 2+3=5, 2+3+23=28, 2+3+23+69=97,408. Thus, {2,5,28,97,408}. We already see that the connection, even if seemingly transparent, if tackled with statistics, would bring results similar to the PNT-based dependence of the number of digits. The output function grows too fast and potential research would be to handle it with yet another (guessed) function to decrease the tempo of growth. This is something I would always omit.

So, we would have the biggest blocker of an n-blocker as well as the smallest one. But it would be crucial to understand what really R-sequence means rather than focus on the statistical approach. By definition, it divides the $\Xi$ matrix into two domains: L-sided and R-sided numbers, itself being the third element, outside R- and L-sided elements. Because every number, if multiplied by 2, would become the smallest of the numbers that have the original number amongst its divisors, the R-numbers (R-sided numbers) are column becoming the smallest of numbers with certain amount of divisors.

The rest of the analysis got disturbed with these tasks. I could not wait to write it. In both cases find the set of values of $a_n$.

$a_n = 3^{k_0}+3^{k_1}+3^{k_2}+...+3^{k_{n-1}}+3^{k_n}$, for $k_0+k_1+...k_{n-1}+k_n = \pi$.

$a_n = e^{ik_0}+e^{ik_1}+e^{ik_2}+...+e^{ik_{n-1}}+e^{ik_n}$, for $k_0+k_1+...k_{n-1}+k_n = \pi$.