Journals / Mathematical Sciences and Applications E-Notes / 2015 / Cilt: 3 - Sayı: 2

ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS

Pages
20–26
Publication Date
2015-10-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, two efficient tests are introduced as to whether or not a positive integer is k-Fibonacci or k-Lucas.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study we investigate some properties of the k-Fibonacci and k-Lucas sequences which are generalize the classical Fibonacci and Lucas sequences.
📊
Key Findings & Data:In this study we investigate some properties of the k-Fibonacci and k-Lucas sequences which are generalize the classical Fibonacci and Lucas sequences.
💡
Conclusion & Impact:Moreover, two efficient tests are introduced as to whether or not a positive integer is k-Fibonacci or k-Lucas.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:k-Fibonacci number · k-Lucas number · Binet formula

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.

🔖

Cite This Article

ÖZGÜR, N. Y., KAYMAK, Ö. Ö. (2015). ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Mathematical Sciences and Applications E-Notes, Cilt: 3 - Sayı: 2, 20–26. https://ajindex.com/articles/690775

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  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