The transformation of the sequence 2n-1 when applying the Collatz algorithm

The transformation of the sequence 2n-1 when applying the Collatz algorithm, is described in this document using modular arithmetic (mod 2, mod 3 and mod 6). As sequences of the form xn-y can either be odd number sequences, even number sequences or mixed parity sequences, a methodology to split these mixed parity sequences into odd and even sub sequences, is introduced as well. Only the transformation of the sequence 2n-1 is described because it represents all positive odd integers. Also, the proof that the conjecture's validity for odd numbers implies its validity for even numbers is given in this document.