Research Article
BibTex RIS Cite
Year 2015, , 20 - 26, 30.10.2015
https://doi.org/10.36753/mathenot.421323

Abstract

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

ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS

Year 2015, , 20 - 26, 30.10.2015
https://doi.org/10.36753/mathenot.421323

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. 

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
There are 13 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Nihal Yilmaz Özgür This is me

Öznur Öztunç Kaymak This is me

Publication Date October 30, 2015
Submission Date July 8, 2015
Published in Issue Year 2015

Cite

APA Özgür, N. Y., & Kaymak, Ö. Ö. (2015). ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Mathematical Sciences and Applications E-Notes, 3(2), 20-26. https://doi.org/10.36753/mathenot.421323
AMA Özgür NY, Kaymak ÖÖ. ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Math. Sci. Appl. E-Notes. October 2015;3(2):20-26. doi:10.36753/mathenot.421323
Chicago Özgür, Nihal Yilmaz, and Öznur Öztunç Kaymak. “ON DETERMINATION OF K-FIBONACCI AND K-LUCAS NUMBERS”. Mathematical Sciences and Applications E-Notes 3, no. 2 (October 2015): 20-26. https://doi.org/10.36753/mathenot.421323.
EndNote Özgür NY, Kaymak ÖÖ (October 1, 2015) ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Mathematical Sciences and Applications E-Notes 3 2 20–26.
IEEE N. Y. Özgür and Ö. Ö. Kaymak, “ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS”, Math. Sci. Appl. E-Notes, vol. 3, no. 2, pp. 20–26, 2015, doi: 10.36753/mathenot.421323.
ISNAD Özgür, Nihal Yilmaz - Kaymak, Öznur Öztunç. “ON DETERMINATION OF K-FIBONACCI AND K-LUCAS NUMBERS”. Mathematical Sciences and Applications E-Notes 3/2 (October 2015), 20-26. https://doi.org/10.36753/mathenot.421323.
JAMA Özgür NY, Kaymak ÖÖ. ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Math. Sci. Appl. E-Notes. 2015;3:20–26.
MLA Özgür, Nihal Yilmaz and Öznur Öztunç Kaymak. “ON DETERMINATION OF K-FIBONACCI AND K-LUCAS NUMBERS”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 2, 2015, pp. 20-26, doi:10.36753/mathenot.421323.
Vancouver Özgür NY, Kaymak ÖÖ. ON DETERMINATION OF k-FIBONACCI AND k-LUCAS NUMBERS. Math. Sci. Appl. E-Notes. 2015;3(2):20-6.

Cited By

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.