New Observations and Data on M&m Sequences
Mentor:Scott Annin, Professor of Mathematics, California State University Fullerton
A mean and median sequence (known as an M&m sequence) begins with any three real numbers, and successive terms are determined in such a way that the nth term satisfies the condition that the mean of the first n terms equals the median of the first n-1 terms. No examples of M&m sequences are known that fail to eventually become stable. Using a C++ program to generate large quantities of M&m sequences we collect data, look for patterns, and make some new observations about these sequences. We also present a few tricks for tackling the conjecture that all M&m sequences stabilize. Finally, we present a few interesting questions about other sequences that are related to M&m sequences.