Infinite product involves the Tribonacci numbers

Kantaphon Kuhapatanakul, Pornpawee Anantakitpaisal, Chanokchon Onsri and Suriya Na nhongkai
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 4, Pages 78—81
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Authors and affiliations

Kantaphon Kuhapatanakul
Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok, Thailand

Pornpawee Anantakitpaisal
Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok, Thailand

Chanokchon Onsri
Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok, Thailand

Suriya Na nhongkai
Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok, Thailand

Abstract

In this short note, we discuss the integer part for the inverse of 1 − Πk=n(1 − 1/Tk), where Tn are the Tribonacci numbers. We also consider a similar formula for the Tribonacci numbers with indices in arithmetic progression and give an open problem of the Diophantine equation about the Tribonacci numbers.

Keywords

  • Tribonacci number
  • Infinite product
  • Diophantine equation

    AMS Classification

    • 11B39
    • 11D99

    References

    1. Anantakitpaisal, P., & Kuhapatanakul, K. (2016) Reciprocal sums of the Tribonacci numbers, J. Integer Seq., 19(2016), Article 16.2.1.
    2. Ohtsuka, H. (2015) Solution H-734 “Integer Parts of Reciprocals of Tails of Infinite Products with Fibonacci Numbers”, The Fibonacci Quarterly, 53(1), 89.
    3. N. J. A. Sloane, The On-line Encyclopedia of Integer Sequences, published electronically at http://oeis.org

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      Cite this paper

      APA

      Kuhapatanakul, K., Anantakitpaisal, P., Onsri, C. & Na nhongkai, S. (2016). Infinite product involves the Tribonacci numbers, Notes on Number Theory and Discrete Mathematics, 22(4), 78-81.

      Chicago

      Kuhapatanakul, Kantaphon, Pornpawee Anantakitpaisal, Chanokchon Onsri and Suriya Na nhongkai “Infinite Product Involves the Tribonacci Numbers.” Notes on Number Theory and Discrete Mathematics 22, no. 4 (2016): 78-81.

      MLA

      Kuhapatanakul, Kantaphon, Pornpawee Anantakitpaisal, Chanokchon Onsri and Suriya Na nhongkai, “Infinite Product Involves the Tribonacci Numbers.” Notes on Number Theory and Discrete Mathematics 22.4 (2016): 78-81. Print.

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