TY - UNPD A1 - Koch, Christian A1 - Sultanow, Eldar A1 - Cox, Sean T1 - Divisions by Two in Collatz Sequences N2 - The Collatz conjecture is an unsolved number theory problem. We approach the question by examining the divisions by two that are performed within Collatz sequences. Aside from classical mathematical methods, we use techniques of data science. Based on the analysis of 10,000 sequences we show that the number of divisions by two lies within clear boundaries. Building on the results, we formulate and prove several theorems on the occurrence of cycles and the termination of Collatz sequences. The findings are useful for further investigations and could form the basis for a comprehensive proof of the conjecture. KW - Collatz Conjecture KW - Number Theory KW - Data Science KW - Collatz-Problem KW - Zahlentheorie KW - Data Science Y1 - 2020 UR - https://opus4.kobv.de/opus4-ohm/frontdoor/index/index/docId/617 UR - https://nbn-resolving.org/urn:nbn:de:bvb:92-opus4-6172 ER -