More new properties of modified Jacobsthal and Jacobsthal–Lucas numbers

Julius Fergy T. Rabago
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 2, Pages 43—54
Download full paper: PDF, 192 Kb

Details

Authors and affiliations

Julius Fergy T. Rabago
Institute of Mathematics, College of Science
University of the Philippines Diliman
Quezon City 1101, Philippines

Abstract

We present some new elementary properties of modified Jacobsthal (Atanassov, 2011) and Jacobsthal–Lucas numbers (Shang, 2012).

Keywords

  • Jacobsthal numbers
  • Jacobsthal–Lucas numbers
  • Second-order recurrence sequence

AMS Classification

  • 11B39
  • 11B37

References

  1. Arunkumar, S., Kannan, V., & Srikanth, R. (2013) Relations on Jacobsthal numbers, Noteson Number Theory and Discrete Mathematics, 19(3), 21–23.
  2. Atanassov, K. T. (2011) Remark on Jacobsthal numbers, Part 2, Notes on Number Theoryand Discrete Mathematics, 17(2), 37–39.
  3. Atanassov, K. T. (2012) Short remarks on Jacobsthal numbers, Notes on Number Theoryand Discrete Mathematics, 18(2), 63–64.
  4. Behera, A., & Panda, G. K. (1999) On the square roots of triangular numbers, The FibonacciQuaterly, 37(2), 98–105.
  5. Chandra, P., & Weisstein, E.W. Fibonacci Number. MathWorld – A Wolfram Web Resource.Retrieved from http://mathworld.wolfram.com/FibonacciNumber.html.
  6. Lucas, E. (1878) Th´eorie des Fonctions Num´eriques Simplement P´eriodiques, American Journal of Mathematics, 1, 184–240, 289–321; reprinted as “The Theory of Simply Periodic Numerical Functions”, Santa Clara, CA: The Fibonacci Association, 1969.
  7. Panda, G. K. (2006) Some fascinating properties of balancing numbers, Applications of Fibonacci Numbers, Congressus Numerantium, 194, 185–190.
  8. Panda, G. K., & Rout, S. S. (2012) A Class of Recurrent Sequence Exhibiting Some Exciting Properties of Balancing Numbers,World Academy of Science, Engineering, and Technology, 61, 164–166.
  9. Popov, B. S. (1986) Summation of Reciprocal Series of Numerical Functions of Second-Order, The Fibonacci Quarterly, 24(1), 17–21.
  10. Rabago, J. F. T. (2013) A note on modified Jacobsthal and Jacobsthal–Lucas numbers, Notes on Number Theory and Discrete Mathematics, 19(3), 15–20.
  11. Rabago, J. F. T. (2014) Some new properties of modified Jacobsthal and Jacobsthal–Lucas numbers, Proceedings of the 3rd International Conference on Mathematical Sciences ICMS3, AIP Conf. Proc., 1602, 805–818.
  12. Rabinowitz, S. (1998) A Note on the Sum Σ 1/wkwn, Missouri Journal of Mathematical Sciences, 10, 141–146.
  13. Shang, Y. (2012) On the modifications of the Pell-Jacobsthal numbers, Scientia Magna, 8(3), 68–70.

Related papers

Cite this paper

APA

Rabago, J. F. T. (2015). More new properties of modified Jacobsthal and Jacobsthal–Lucas numbers. Notes on Number Theory and Discrete Mathematics, 21(2), 43-54.

Chicago

Rabago, Julius Fergy T. “More New Properties of Modified Jacobsthal and Jacobsthal–Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 21, no. 2 (2015): 43-54.

MLA

Rabago, Julius Fergy T. “More New Properties of Modified Jacobsthal and Jacobsthal–Lucas Numbers.” Notes on Number Theory and Discrete Mathematics 21.2 (2015): 43-54. Print.

Comments are closed.