This talk will focus on the research projects conducted with my undergraduate students on numerical sequences. My introduction to research in this area began in June 2018, when I stumbled on a YouTube video by a famous astrologer, named David Cochrane, and he made some number theoretic connections between the Fibonacci sequence and astrology. Cochrane is no mathematician, but his video presented a number of conjectures, all of a mathematical nature, which immediately became a source of research for my students that year. That work has been published, and each year since then, my new undergraduate students and I completed research projects on various numerical sequences, leading to publications as well as fond memories. A prominent part of this talk focuses on the most recent publication, which is a joint work with my research student Janee Schrader and my external collaborator Dr.~Jurgen Spilker in Germany. We consider six different linear recurrence sequences: Pell $P_n$, associated Pell $Q_n$, balancing $B_n$, Lucas-balancing $C_n$, cobalancing $b_n$, and Lucas-cobalancing $c_n$ numbers. We compute a closed form for the greatest common divisor of all sums of $k$ consecutive numbers coming from each of these six sequences. This talk should be accessible to a wide audience. I also promise that the word ``tantalizing'' was very intentionally placed in the talk title; these projects will excite your senses and may lead you to do your own explorations of these fascinating sequences!
Tantalizing Adventures with my Undergraduate Research Students on Numerous Numerical Sequences
aBa Mbirika, University of Wisconsin-Eau ClaireAuthors: aBa Mbirika, Janee Schrader, and J"urgen Spilker
2023 AWM Research Symposium
Number Theory at Primarily Undergraduate Institutions [Organized by Bella Tobin and Leah Sturman]