The importance of recurrence sequences hardly needs to be explained. Their study is
plainly of intrinsic interest and has been a central part of number theory for many years …

The 3x+ 1 Problem is perhaps today's most enigmatic unsolved mathematical problem: it
can be explained to child who has learned how to divide by 2 and multiply by 3, yet there are …

Collatz dynamic systems present a statistical space that can be studied rigorously. In a
previous study, the author presented Collatz space in a unique dynamic numerical mode by …

The 3x+ 1 Problem is perhaps today's most enigmatic unsolved mathematical problem: it
can be explained to child who has learned how to divide by 2 and multiply by 3, yet there are …

A class of transformations named as Integral Value Transformation (IVT) on where denotes
the set of natural numbers along with zero is introduced. Using IVT an iterative scheme is …

Davant de l'enunciat de la conjectura 3x+ 1 és fàcil que se'ns escapi el comentari de
«sembla molt senzill». Però, com en tants d'altres problemes d'aquesta mena, el cert és que …

In 1937, shortly after the mathematician Lothar Collatz obtained his doctorate, he wrote
down a problem in his notebook that later became known as Collatz'problem or the (3x+ 1) …

In this work, we investigate the odd Collatz sequences (odd sequences arising from the 3n+
1 problem) and use binary arithmetic to provide proof of some results in the 3n+ 1 problem …

Andrei et al. have shown in 2000 that the graph $\boldsymbol {\mathrm {C}} $ of the Collatz
function starting with root $8 $ after the initial loop is an infinite binary tree $\boldsymbol …

On the non-trivial cycles in Collatz’s problem Page 1 SUT Journal of Mathematics Vol. 41, No.
1 (2005), 31–41 On the non-trivial cycles in Collatz’s problem Florian Luca (Received …