A STUDY ON GENERALIZED 5-PRIMES NUMBERS


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DOI:

https://doi.org/10.26900/jsp.4.017%20

Keywords:

5-primes numbers, Lucas 5-primes numbers, generalized Pentanacci numbers, modied 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.

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References

[1] Howard, F.T., Saidak, F., Zhou’s Theory of Constructing Identities, Congress Numer. 200, 225-237, 2010.
[2] Kalman, D., Generalized Fibonacci Numbers By Matrix Methods, Fibonacci Quarterly, 20(1), 73-76, 1982.
[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] 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] Natividad, L. R., On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3 (2), 2013.
[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] Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/
[8] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 45-56, 2019.
[9] Soykan, Y., Sum Formulas For Generalized Fifth-Order Linear Recurrence Sequences, Journal of Advances in Mathematics and Computer Science, 34(5), 1-14, 2019, Article no.JAMCS.53303, ISSN: 2456-9968, DOI: 10.9734/JAMCS/2019/v34i530224.  

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Published

2020-08-05 — Updated on 2020-08-06

How to Cite

SOYKAN, Y. (2020). A STUDY ON GENERALIZED 5-PRIMES NUMBERS. HEALTH SCIENCES QUARTERLY, 4(3), 185–202. https://doi.org/10.26900/jsp.4.017

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Letter to the Editor