Volume 30 ▶ Number 1 ▷ Number 2 ▷ Number 3 (Online First)
On the pulsating Padovan sequence
Original research paper. Pages 1–7
Orhan Dişkaya and Hamza Menken
Full paper (PDF, 182 Kb) | Abstract
Discatenated and lacunary recurrences
Original research paper. Pages 8–19
Hakan Akkuş, Ömür Deveci, Engin Özkan and Anthony G. Shannon
Full paper (PDF, 944 Kb) | Abstract
Proving the existence of Euclidean knight’s tours on n × n × ⋯ × n chessboards for n < 4
Original research paper. Pages 20–33
Marco Ripà
Full paper (PDF, 1613 Kb) | Abstract
Our counterintuitive outcome follows from the observation that we can alternatively define a 2D knight as a piece that moves from one square to another on the chessboard by covering a fixed Euclidean distance of so that also the statement of Theorem 3 in [Erde, J., Golénia, B., & Golénia, S. (2012), The closed knight tour problem in higher dimensions, The Electronic Journal of Combinatorics, 19(4), #P9] does not hold anymore for such a Euclidean knight, as long as a 2 × 2 × ⋯ × 2 chessboard with at least 27 cells is given. Moreover, we construct a classical closed knight’s tour on whose arrival is at a distance of 2 from , and then we show a closed Euclidean knight’s tour on .
Some results on geometric circulant matrices involving the Leonardo numbers
Original research paper. Pages 34–46
Samet Arpacı and Fatih Yılmaz
Full paper (PDF, 316 Kb) | Abstract
Second-order linear recurrences with identically distributed residues modulo pe
Original research paper. Pages 47–66
Lawrence Somer and Michal Křížek
Full paper (PDF, 257 Kb) | Abstract
Generalization of the 2-Fibonacci sequences and their Binet formula
Original research paper. Pages 67–80
Timmy Ma, Richard Vernon and Gurdial Arora
Full paper (PDF, 256 Kb) | Abstract
Distance between consecutive elements of the multiplicative group of integers modulo n
Original research paper. Pages 81–99
Steven Brown
Full paper (PDF, 314 Kb) | Abstract
In this paper, we are mostly concerned with providing formulas to count the number of gaps of a given even length in which we note . This work, presented with different notations is closely related to [5]. We prove the formulas in three steps. Although only the last step relates to the problem of gaps in the Eratosthenes sieve (see Section 3.2.2) the previous formulas may be of interest to study occurrences of defined gaps sequences.
- For a positive integer , we prove a general formula based on the inclusion-exclusion principle to count the number of occurrences of configurations1 in any subset of . (see Equation (7) in Theorem 2.1).
- For a square-free integer , we particularize this formula when the subset of interest is . (see Equation (11) in Theorem 3.2).
- For a prime and its primorial , we particularize the formula again to study gaps in . Given a positive integer representing a distance on the circle, we give formulas to count the number of gaps of length between elements of (see Equation (15) and Section 4.1).
In addition, we provide a formula (see Equation (27) in Theorem 5.1) to count the number of occurrences of gaps of an even length that contain exactly elements of .
1 A defined sequence of gaps between the elements of the subset; this is referred to as a constellation in [5].
Some new properties of hyperbolic k-Fibonacci and k-Lucas octonions
Original research paper. Pages 100–110
A. D. Godase
Full paper (PDF, 218 Kb) | Abstract
On certain arithmetical products involving the divisors of an integer
Original research paper. Pages 111–115
József Sándor
Full paper (PDF, 210 Kb) | Abstract
Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, I
Original research paper. Pages 116–140
A. M. S. Ramasamy
Full paper (PDF, 347 Kb) | Abstract
On the characterization of rectangular duals
Original research paper. Pages 141–149
Vinod Kumar and Krishnendra Shekhawat
Full paper (PDF, 181 Kb) | Abstract
Generalized perfect numerical semigroups
Original research paper. Pages 150–162
Mohammad Zmmo and Nesrin Tutaş
Full paper (PDF, 461 Kb) | Abstract
Characterization of prime and composite numbers using the notion of successive sum of integers and the consequence in primality testing
Original research paper. Pages 163–169
Fateh Mustapha Dehmeche, Douadi Mihoubi and Lahcene Ladjelat
Full paper (PDF, 579 Kb) | Abstract
Factorial polynomials and associated number families
Original research paper. Pages 170–178
Alfred Schreiber
Full paper (PDF, 195 Kb) | Abstract
Two arithmetic functions related to Euler’s and Dedekind’s functions
Original research paper. Pages 179–183
Krassimir Atanassov
Full paper (PDF, 225 Kb) | Abstract
Metallic means and Pythagorean triples
Original research paper. Pages 184–194
Chetansing Rajput and Hariprasad Manjunath
Full paper (PDF, 359 Kb) | Abstract
Distribution of constant terms of irreducible polynomials in ℤp[x] whose degree is a product of two distinct odd primes
Original research paper. Pages 195–210
Sarah C. Cobb, Michelle L. Knox, Marcos Lopez, Terry McDonald, and Patrick Mitchell
Full paper (PDF, 280 Kb) | Abstract
Editorial Correction to “A note on a generalization of Riordan’s combinatorial identity via a hypergeometric series approach” [Notes on Number Theory and Discrete Mathematics, 2023, Volume 29, Number 3, Pages 421–425]
Editorial correction. Pages 211–212
Kunle Adegoke
Editorial correction (PDF, 161 Kb)