Julius Fergy T. Rabago

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 21, 2015, Number 2, Pages 43–54

**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

- Arunkumar, S., Kannan, V., & Srikanth, R. (2013) Relations on Jacobsthal numbers, Noteson Number Theory and Discrete Mathematics, 19(3), 21–23.
- Atanassov, K. T. (2011) Remark on Jacobsthal numbers, Part 2, Notes on Number Theoryand Discrete Mathematics, 17(2), 37–39.
- Atanassov, K. T. (2012) Short remarks on Jacobsthal numbers, Notes on Number Theoryand Discrete Mathematics, 18(2), 63–64.
- Behera, A., & Panda, G. K. (1999) On the square roots of triangular numbers, The FibonacciQuaterly, 37(2), 98–105.
- Chandra, P., & Weisstein, E.W. Fibonacci Number. MathWorld – A Wolfram Web Resource.Retrieved from http://mathworld.wolfram.com/FibonacciNumber.html.
- 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.
- Panda, G. K. (2006) Some fascinating properties of balancing numbers, Applications of Fibonacci Numbers, Congressus Numerantium, 194, 185–190.
- 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.
- Popov, B. S. (1986) Summation of Reciprocal Series of Numerical Functions of Second-Order, The Fibonacci Quarterly, 24(1), 17–21.
- 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. - 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.
- Rabinowitz, S. (1998) A Note on the Sum Σ 1/
*w*, Missouri Journal of Mathematical Sciences, 10, 141–146._{kwn} - Shang, Y. (2012) On the modifications of the Pell-Jacobsthal numbers, Scientia Magna, 8(3), 68–70.

## Related papers

## Cite this paper

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.