Raghib Abusaris 1,*, Sai’da Atawna 2
1 Department of Epidemiology and Biostatistics, College of Public Health and Health Informatics, King Saud bin Abdelaziz University for Health Science, Riyadh, Saudi Arabia.
2 Department of Economics Imam Malik Academy, Basaksehir, Istanbul, Turkey.
*Corresponding author: Raghib Abusaris, Department of Epidemiology and Biostatistics, College of Public Health and Health Informatics, King Saud bin Abdelaziz University for Health Science, Riyadh, Saudi Arabia.
Abstract
In this paper, we investigate the asymptotic behavior of the sequences generated by iterating the process of summing the powers modulo b - 1 in base-b system where b is a power of prime. In particular, we identify modular happy numbers. Following the spirit of happy number [1, p. 374], a number is called b-modular happy if the sequence obtained by iterating the process of summig the powers modulo (b - 1) in base-b system ends with 1.
References
[1] Guy, R. (2004). Unsolved problems in number theory (3rd ed.). New York, NY: Springer.
[2] Abu-Saris, R. & Bayyati, O. (2018), On Modular Happy Numbers. Notes on Number.
Theory and Discrete Mathematics, 24: 117124. DOI: 10.7546/nntdm.2018.24.2.117-124.
[3] Rosen, K. H. (2019). Discrete mathematics and its applications (8th ed.). New York, NY: McGraw-Hill.
[4] Weisstein, E. W. (2020). Periodic sequence. Retrieved from http://mathworld.wolfram.com/PeriodicSequence. html.
[5] Keef, P., & Guichard, D. (2018). An Introduction to Higher Mathematics, San Francisco, CA: Creative Commons.
[6] Gilmer, J. (2013). On the density of happy numbers. Integers,13, A48: 1-25.
[7] Trevio, E. & Zhylinski, M. (2019). On generalizing happy numbers to fractional-base number systems. Involve, 12: 11431151.
[8] Williams, E. S. (2016). Further Generalizations of Happy Numbers. Retrieved from http://sections.maa.org/ epadel/awards/studentpaper/winners/2016Williams.pdf.
How to cite this paper
On Modular Happy Numbers II
How to cite this paper: Raghib Abusaris, Sai’da Atawna. (2020) On Modular Happy Numbers II. Journal of Applied Mathematics and Computation, 4(2), 14-17.
DOI: http://dx.doi.org/10.26855/jamc.2020.06.001
