Properties of Generalized 6-primes Numbers

Main Article Content

Yüksel Soykan


In this paper, we introduce the generalized 6-primes sequence and we deal with, in detail, three special cases which we call them 6-primes, Lucas 6-primes and modified 6-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.

Hexanacci numbers, 6-primes numbers, Lucas 6-primes numbers, modified 6-primes numbers.

Article Details

How to Cite
Soykan, Y. (2020). Properties of Generalized 6-primes Numbers. Archives of Current Research International, 20(6), 12-30.
Original Research Article


Natividad LR. On solving fibonacci-like sequences of fourth, fifth and sixth order. International Journal of Mathematics and Computing. 2013;3(2).

Rathore GPS, Sikhwal O, Choudhary R. Formula for finding nth term of Fibonaccilike sequence of higher order. International Journal of Mathematics and its Applications. 2016;4(2-D):75-80.

Howard FT, Saidak F. Zhou’s theory of constructing identities. Congress Numer. 2010;200:225-237.

Soykan Y. On generalized 2-primes numbers. Asian Journal of Advanced Research and Reports. 2020;9(2):34-53. DOI: 10.9734/AJARR/2020/v9i230217

Soykan Y. On generalized Grahaml numbers. Journal of Advances in Mathematics and Computer Science. 2020;35(2):42-57. DOI: 10.9734/JAMCS/2020/v35i230248

Soykan Y. On generalized reverse 3-primes numbers. Journal of Scientific Research and Reports. 2020;26(6):1-20. DOI: 10.9734/JSRR/2020/v26i630267

Soykan Y. On generalized 4-primes numbers. Int. J. Adv. Appl. Math. and 29Soykan; ACRI, 20(6): 12-30, 2020; Article no.ACRI.60386 Mech. 2020;7(4):20-33. ISSN: 2347-2529

Soykan Y. A study on generalized 5-primes numbers. Journal of Scientific Perspectives. 2020;4(3):185-202. DOI:

Mazur B, William Stein W. Prime numbers and the Riemann hypothesis. Cambridge University Press; 2016.

Sloane NJA. The on-line encyclopedia of integer sequences. Available:

Stanley RP. Generating functions, studies in combinatorics. MAA Studies in Mathematics, Math. Assoc. of America, Washington, D.C. 1978;17:100-141.

Soykan Y. Simson identity of generalized m-step Fibonacci numbers. Int. J. Adv. Appl. Math. and Mech. 2019;7(2):45-56.

Soykan Y. A study on sum formulas of generalized sixth-order linear recurrence sequences. Submitted.

Kalman D. Generalized Fibonacci numbers by matrix methods. Fibonacci Quarterly. 1982;20(1):73-76.