Version 1
: Received: 18 June 2020 / Approved: 21 June 2020 / Online: 21 June 2020 (14:52:12 CEST)
Version 2
: Received: 12 August 2020 / Approved: 14 August 2020 / Online: 14 August 2020 (03:44:15 CEST)
How to cite:
Khare, M.; Chitta, K. Successive Addition of Digits of an Integer Number: On Properties and Role in Studying Distribution of Primes. Preprints2020, 2020060276. https://doi.org/10.20944/preprints202006.0276.v1
Khare, M.; Chitta, K. Successive Addition of Digits of an Integer Number: On Properties and Role in Studying Distribution of Primes. Preprints 2020, 2020060276. https://doi.org/10.20944/preprints202006.0276.v1
Khare, M.; Chitta, K. Successive Addition of Digits of an Integer Number: On Properties and Role in Studying Distribution of Primes. Preprints2020, 2020060276. https://doi.org/10.20944/preprints202006.0276.v1
APA Style
Khare, M., & Chitta, K. (2020). Successive Addition of Digits of an Integer Number: On Properties and Role in Studying Distribution of Primes. Preprints. https://doi.org/10.20944/preprints202006.0276.v1
Chicago/Turabian Style
Khare, M. and Kalyanlakshmi Chitta. 2020 "Successive Addition of Digits of an Integer Number: On Properties and Role in Studying Distribution of Primes" Preprints. https://doi.org/10.20944/preprints202006.0276.v1
Abstract
Successive-addition-of-digits-of-a-number(SADN) refers to the process of adding up the digits of an integer number until a single digit is obtained. Concept of SADN has been occasionally identified but seldom employed in extensive mathematical applications. This paper discusses SADN and its properties in terms of addition, subtraction and multiplication. Further, the paper applies the multiplication-property of SADN to understand the distribution of prime numbers. For this purpose the paper introduces three series of numbers -S1, S3 and S5 series- into which all odd numbers can be placed, depending on their SADN and the rationale of such classification. Extending the analysis the paper explains how composite numbers of the S1 and S5 series can be derived. Based on this discussion it concludes that even as the concept of SADN is rather simple in its formulation and appears as an obvious truism but a profound analysis of the properties of SADN in terms of fundamental mathematical functions reveals that SADN holds a noteworthy position in number theory and may have significant implications for unfolding complex mathematical questions like understanding the distribution of prime numbers and Goldbach-problem.
Keywords
Primes; Distribution of Primes; Primes and integers; Additive questions involving primes; Number representations
Subject
Computer Science and Mathematics, Logic
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.