![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
Abstract
A general algorithm is developed for a specific algebraic operation on integer numbers carried out iteratively. The operation is shown pictorially by a chain-necklace diagram. The properties of such diagrams are mentioned. Two special cases, namely Collatz's and Nollatz's conjectures, are discussed in detail. The former conjecture gives a full-length sequence only for restricted numbers. A new generalized conjecture is stated and some logical thoughts are given.
DISCLOSURE STATEMENT
No potential conflict of interest was reported by the author.
Additional information
Notes on contributors
T. S. Rathore
T S Rathore received BSc (Engg), ME and PhD from Indore University, Indore. He served SGSITS, Indore, IIT Bombay, St Francis Institute of Technology, Borivali and IIT Goa. He was a post-doctoral fellow at the Concordia University, Canada, and a visiting researcher at the University of South Australia, Adelaide. He was an ISTE visiting professor (2005–2007). He has published and presented several research papers. Authored the book Digital Measurement Techniques, Narosa Publishing House, India and Alpha Science International Pvt Ltd, UK. The book is translated into Russian and Hindi. He is the co-author of the 3rd revised edition of Network Analysis with M E Van Valkenburg. Was the guest editor of the special issue of Journal of IE on Instrumentation Electronics (1992). He was an editor of IETE Journal of Education (2012–2017). He has served IETE Mumbai Centre as Secretary, Vice-Chairman and Chairman. He has received several academic awards. Details are available at www.ee.iitb.ac.in/wiki/faculty/tsrathor.