More on the Fascinating Characterizations of Mulatu’s Numbers

Background The discoveries of Mulatu’s numbers, better known as Mulatu’s sequence, represent revolutionary contributions to the mathematical world. His best-known work is Mulatu’s sequence, in which each new number is the sum of the two preceding numbers. When various operations and manipulations are performed on the numbers in this sequence, beautiful and incredible patterns begin to emerge. This study aimed to identify novel characterizations of Mulatu’s numbers. Methods This study employed a multi-faceted approach to investigate characterizations of Mulatu’s numbers. Mathematical proof techniques such as principle of mathematical induction, proof by contradiction and direct proof were utilized to substantiate findings. GNU Octave (version 9, (1)) software was applied to verify the existence, classify, and conduct computational investigations of findings prior to formal proofs. Results In this study, we provided several characterizations of Mulatu’s numbers. We also investigated the properties and patterns of these fascinating numbers. Moreover, we have also shown that, similar to Fibonacci’s numbers, Mulatu’s numbers also give the so-called golden ratio, which is most applicable in numerical optimization. Furthermore, we formulated a relation among Mulatu’s numbers, Fibonacci numbers, and Lucas numbers. Finally, we provided a generating function for the Mulatu numbers. Conclusions In this study, we uncovered novel characterizations of Mulatu’s numbers and introduced a generating function for them. We investigated relationship between Mulatu’s numbers and the golden ratio. The results discussed offer valuable insights and enhance our understanding of their properties. Furthermore, these findings play a vital role in the boarder context of mathematical sequences, contributing significantly to the field.