Finite search for blockers in R-sequence

All blockers are of form {3^x+2n+1}. Thus, we have (depending on blocker) n in sets {1,3,4,9,11}, {4,10,13,14,18,28,30,34}. These sets are as complex (to understand) as the blocker sequences, ie. their story is equivalent (in terms of difficulty of  understanding) to the blocker story.

28 = 3^3 + 2*0 + 1;    3,0

30 = 3^3 + 2*1 + 1; 3,1

84 = 3^4 + 2*1 + 1; 4,1
88 = 3^4 + 2*3 + 1;    4,3
90 = 3^4 + 2*4 + 1;       4,4
100= 3^4 + 2*9 + 1;           4,9
104= 3^4 + 2*11+ 1;            4,11

252= 3^5 + 2*4 + 1;             5,4
264= 3^5 + 2*10+ 1;     5,10
270= 3^5 + 2*13+ 1;        5,13
272= 3^5 + 2*14+ 1;     5,14
280= 3^5 + 2*18+ 1;        5,18
300= 3^5 + 2*28+ 1;             5,28
304= 3^5 + 2*30+ 1;               5,30
312= 3^5 + 2*34+ 1;             5,34

If we look at the form as if it was {3^x+A}, then we have: {2,4,5,10,12}, {5,11,14,15,19,29,31,35}. The second part of the sumation involves an odd number (albeit not necessarily prime). Yet another approach for analyzing {3^x+A} form would be to use the Lambert W function. However, I cannot yet see how that would help in distinguishing the most crucial facts about the form.

Knowing all the n-blockers, we’d be able to find all the R-sided numbers. The question still remains how R-sequence defines the L-sided numbers, ie. this conondrum beneath the Xi matrix imposes the limitations on prime distribution, hence the more holistic approach would be necessary.

It is worth highlighting that the reticent R-sequence, namely each n-blocker from the sequence, refer to n-th prime number. Finding the heuristics for the relation might be useful in terms of the PNT. Assuming that we know both, ie.  how many n-blockers exist before the next 3^x and the relation between the n-th prime and the n-th blocker, we would be able to predict the n-th prime.

In the context of the analysis, I would like to ask one question. How can we deduce number’s dimension by the look at the digits of the very number? As you know, we might find new ways to find divisibility by certain numbers (looking at digits), and that somehow leads to the solution. But, can we generalize the problem and tackle it in such a way: we don’t care about divisors, we care about the number of divisors. This number of divisors refers to the number of dimensions the number has if we wanted to describe it geometrically using earlier shown methodologies.

Another interesting aspect of problem solving I’d been thinking of recently is that for the descent we could use the fact that sum of two numbers is rational only if both numbers are rational as well as it’s natural only if two numbers that sum up to it are natural (assuming integer domain of definition).

This approach to the infinite descent clearly indicates that all constraints and elements that confine possiblities to certain sets may be attacked using the infinity-based mechanism. If certain function of translation of a sequence changes the character of the very sequence into one that is self-contradicting in some sense, then we may attack the problem for which this sequence represents e.g. the number of solutions or the solutions themselves.


About misha

Imagine a story that one can't believe. Hi. Life changes here. Small things only.
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