Research Article

A STUDY ON GENERALIZED 5-PRIMES NUMBERS

Volume: 4 Number: 3 August 19, 2020
EN

A STUDY ON GENERALIZED 5-PRIMES NUMBERS

Abstract

In this paper, we introduce the generalized 5-primes numbers sequences and we deal with, in detail, three special cases which we call them 5-primes, Lucas 5-primes and modified 5-primes sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences ........................... .................... ....................................   

 2010  Mathematics Subject Classication. 11B39,  11B83.

Keywords

References

  1. [1] Howard, F.T., Saidak, F., Zhou’s Theory of Constructing Identities, Congress Numer. 200, 225-237, 2010.
  2. [2] Kalman, D., Generalized Fibonacci Numbers By Matrix Methods, Fibonacci Quarterly, 20(1), 73-76, 1982.
  3. [3] Kiliç, E., Stanica, P., A Matrix Approach for General Higher Order Linear Recurrences, Bulletin of the Malaysian Mathematical Sciences Society, (2) 34(1), 51.67, 2011.
  4. [4] Melham, R. S., Some Analogs of the Identity , F_n^2+F_(n+1)^2=F_(2n+1)^2 Fibonacci Quarterly, 305-311, 1999.
  5. [5] Natividad, L. R., On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3 (2), 2013.
  6. [6] Rathore, G.P.S., Sikhwal, O., Choudhary, R., Formula for finding nth Term of Fibonacci-Like Sequence of Higher Order, International Journal of Mathematics And its Applications, 4 (2-D), 75-80, 2016.
  7. [7] Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/
  8. [8] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 45-56, 2019.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Publication Date

August 19, 2020

Submission Date

March 23, 2020

Acceptance Date

July 31, 2020

Published in Issue

Year 2020 Volume: 4 Number: 3

APA
Soykan, Y. (2020). A STUDY ON GENERALIZED 5-PRIMES NUMBERS. Journal of Scientific Perspectives, 4(3), 185-202. https://doi.org/10.26900/jsp.4.017
AMA
1.Soykan Y. A STUDY ON GENERALIZED 5-PRIMES NUMBERS. JSP. 2020;4(3):185-202. doi:10.26900/jsp.4.017
Chicago
Soykan, Yüksel. 2020. “A STUDY ON GENERALIZED 5-PRIMES NUMBERS”. Journal of Scientific Perspectives 4 (3): 185-202. https://doi.org/10.26900/jsp.4.017.
EndNote
Soykan Y (August 1, 2020) A STUDY ON GENERALIZED 5-PRIMES NUMBERS. Journal of Scientific Perspectives 4 3 185–202.
IEEE
[1]Y. Soykan, “A STUDY ON GENERALIZED 5-PRIMES NUMBERS”, JSP, vol. 4, no. 3, pp. 185–202, Aug. 2020, doi: 10.26900/jsp.4.017.
ISNAD
Soykan, Yüksel. “A STUDY ON GENERALIZED 5-PRIMES NUMBERS”. Journal of Scientific Perspectives 4/3 (August 1, 2020): 185-202. https://doi.org/10.26900/jsp.4.017.
JAMA
1.Soykan Y. A STUDY ON GENERALIZED 5-PRIMES NUMBERS. JSP. 2020;4:185–202.
MLA
Soykan, Yüksel. “A STUDY ON GENERALIZED 5-PRIMES NUMBERS”. Journal of Scientific Perspectives, vol. 4, no. 3, Aug. 2020, pp. 185-02, doi:10.26900/jsp.4.017.
Vancouver
1.Yüksel Soykan. A STUDY ON GENERALIZED 5-PRIMES NUMBERS. JSP. 2020 Aug. 1;4(3):185-202. doi:10.26900/jsp.4.017