TY - JOUR
A2 - De Gregorio, Alessandro
AU - Barghout, Kamal
PY - 2019
DA - 2019/08/01
TI - On the Probabilistic Proof of the Convergence of the Collatz Conjecture
SP - 6814378
VL - 2019
AB - A new approach towards probabilistic proof of the convergence of the Collatz conjecture is described via identifying a sequential correlation of even natural numbers by divisions by 2 that follows a recurrent pattern of the form x,1,x,1…, where x represents divisions by 2 more than once. The sequence presents a probability of 50:50 of division by 2 more than once as opposed to division by 2 once over the even natural numbers. The sequence also gives the same 50:50 probability of consecutive Collatz even elements when counted for division by 2 more than once as opposed to division by 2 once and a ratio of 3:1. Considering Collatz function producing random numbers and over sufficient number of iterations, this probability distribution produces numbers in descending order that lead to the convergence of the Collatz function to 1, assuming that the only cycle of the function is 1-4-2-1.
SN - 1687-952X
UR - https://doi.org/10.1155/2019/6814378
DO - 10.1155/2019/6814378
JF - Journal of Probability and Statistics
PB - Hindawi
KW -
ER -