This study extends the domain of Keçeci Numbers, a unique class of sequences generated by a distinctive algorithm, beyond standard number systems into advanced mathematical structures such as neutrosophic and hyperreal numbers. Keçeci Numbers are sequences produced via a recursive algorithm based on a starting value and an incremental scalar, governed by rules of divisibility and primality. The primary objective of this paper is to investigate the behaviour of this deterministic algorithm within ...

This study presents a comparative analysis of static and dynamic number sequences, using the classical Oresme numbers and the novel Keçeci numbers, developed by Mehmet Keçeci, as primary case studies. Static sequences are characterized by a fixed, predictable recurrence relation. The Oresme numbers—the partial sums of the harmonic series (Η_n=∑(k=1)^n 1/k)—exemplify this category. Their generation follows a simple, deterministic rule (Η_n= Η(n-1)+1/n), and their predictable divergence, proven ...