ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS

Year 2015, Volume: 3 Issue: 2, 20 - 26, 30.10.2015

Nihal Yilmaz Özgür Öznur Öztunç Kaymak

https://doi.org/10.36753/mathenot.421323

Cited By: 1

Abstract

In this study we investigate some properties of the k-Fibonacci
and k-Lucas sequences which are generalize the classical Fibonacci and Lucas
sequences. Moreover, two efficient tests are introduced as to whether or not a
positive integer is k-Fibonacci or k-Lucas. 

Keywords

k-Fibonacci number , ; k-Lucas number , Binet formula

References

• [1] Bolat, C. and Köse H., On the properties of k−Fibonacci numbers, Int. J. Contemp. Math. Sciences, 5, 1097-1105, (2010).
• [2] Falcon S., On the k−Lucas Numbers, Int. J. Contemp. Math. Sciences, 6, 1039-1050, (2011).
• [3] Hoggatt V. E., Generalized Zeckendorf theorem, Fibonacci Quart 10, 89-93, (1972).
• [4] James P., When is a number Fibonacci?, Department of Computer Science, Swansea University, January 25, (2009).
• [5] Kalman, D. and Mena, R., The Fibonacci numbers-exposed. Math. Mag. 76, no. 3, 167-181, (2003).
• [6] Cahill N. D., D’Errico J. R., Spence J. S., Complex factorizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 41, no. 1, 13-19, (2003).
• [7] Ismail, M. E. H., One parameter generalizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 46/47, no. 2, 167-180, (2008/09).
• [8] Koshy T., Fibonacci and Lucas numbers with applications, Wiley, (2001).
• [9] Siar Z., Keskin R., Some new identites concerning Generalized Fibonacci and Lucas Numbers, Hacet. J. Math. Stat. 42, no.3, 211-222, (2013).
• [10] Ozgur, N. Y., Ucar S., Oztunc O., Complex Factorizations of the k−Fibonacci and k−Lucas numbers, in press, (2015).
• [11] S. Falcon and A. Plaza, On the Fibonacci k-numbers, ` Chaos, Solitons & Fractals 32, 1615- 1624 (2007).
• [12] S. Falcon and A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, ` Chaos, Solitons & Fractals 33, 38-49 (2007).
• [13] MATLAB trial version 8.5.0. Natick, Massachusetts: The MathWorks Inc., (2015