About the combination of: harmonic intervals built on the 'tetrada', the problem 3x+1 and the fundamental constant 4:3

This paper presents study of problem 3x+1 (Collatz conjecture) 

within which following research has been made:

- numeral sequences of the form \( \frac{2^p}{3^q}\)

- sequence of ordered numeral intervals of the form \(\frac{\left\{ 2^{a(i)} - 2^{b(i)}\right\}}{3} \)

- the operation of combining and decoupling a sequence of numeral intervals

- a geometric interpretation of a sequence of numeral intervals is given

- fractional numeral systems \(2\cap3\) and \(4\cap3\) are considered

- sequence transformation oddness \(4k+3\) and \(4k+1\)

- \(3x+1\) problem solved

- a connection with a prime numbers has been established