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​International Journal of Modern Computation, Information and Communication Technology

ISSN 2581-5954

​May-June 2019, Vol. 2, Issue 5-6, p. 36-42.​​

Arnold's Digitized Summation Technique and Generalized Notion of the Collatz Conjecture
A. Okoth¹, B. Okelo²*
¹School of Informatics and Innovative Systems, ²School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology,P. O. Box 210-40601, Bondo-Kenya.
*Corresponding author’s e-mail: bnyaare@yahoo.com

Abstract

Many mathematicians have studied Collatz conjecture and its applications; however, it remains an open problem in the field of number theory and is interesting to study. In the present paper, we give a generalized notion of Collatz conjecture as per the new notion of Arnold's Digitized Summation Technique which involves adding digits of a number until we are left with only one single digit. Moreover, a detailed description of the first twenty positive integers is given.

Keywords: Positive integers; Arnold's digitized summation technique; Digitized number form; Collatz Conjecture; Hailstone sequence.

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