Volume 14 ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4
A short remark on transcendental numbers
Original research paper. Pages 1–3
Mladen Vassilev-Misanna
Full paper (PDF, 924 Kb) | Abstract
In the paper, an application of the famous Gelfond–Schneider theorem is made.
A Fibonacci cylinder
Original research paper. Pages 4–9
Krassimir T. Atanassov and Anthony G. Shannon
Full paper (PDF, 1457 Kb)
The identification of rows of primes in the modular ring Z6
Original research paper. Pages 10–15
A. G. Shannon
Full paper (PDF, 2618 Kb) | Abstract
The simple function f(n) = ½n(an ± 1), a = 1, 3, 5 with n = 1, 2, …, 200, generated 615 primes of the modular ring Z6. 194 of these were twin primes. Values of n which yielded primes for all f(n) were simply related to the number of primes in a given range.
Some properties of generalized third order Pell numbers
Original research paper. Pages 16–24
A. G. Shannon and C. K. Wong
Full paper (PDF, 59 Kb) | Abstract
This paper considers some properties of the third order recursive sequence defined by the linear recurrence relation
wm,n = 2mwm, n−2 + wm, n−3, n ≥ 3, m = 0, 1, 2,
with appropriate initial conditions. The present work follows on from the case m = 0 (Shannon et al). Relationships with the well-known sequences of Fibonacci, Lucas and Pell are developed. The motivation for the study was to find analogous results to some of the second order classic identities such as, for example, Simson’s identity and Horadam’s Fibonacci number triples.
wm,n = 2mwm, n−2 + wm, n−3, n ≥ 3, m = 0, 1, 2,
with appropriate initial conditions. The present work follows on from the case m = 0 (Shannon et al). Relationships with the well-known sequences of Fibonacci, Lucas and Pell are developed. The motivation for the study was to find analogous results to some of the second order classic identities such as, for example, Simson’s identity and Horadam’s Fibonacci number triples.
