**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 Z**_{6}

*Original research paper. Pages 10—15*

A. G. Shannon

Full paper (PDF, 2618 Kb) | Abstract

The simple function *f*(*n*) = ½*n*(*an* ± 1), *a* = 1, 3, 5 with *n* = 1, 2, …, 200, generated 615 primes of the modular ring Z_{6}. 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

*w*_{m,n} = 2^{m}w_{m, n−2} + *w*_{m, 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.

**Volume 14** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4