There are many more sequences than arithmetic, sequences such as 1,4, 7, 10, 13,... and geometric sequences such as 2, 6, 18, 54, 162, .... In fact, the online encyclopedia of integer sequences now lists about 200,000 different sequences that people have studied. Looking for patterns in sequences is an enjoyable activity that people with any level of mathematical training can productively pursue.
The Graham sequence is one such sequence, and it is the topic of this activity. A hand-out and mentor guide are attached, as is a key connecting this to the Common Core State Standards in Math. This lesson is relates to the prime factorization. As such, it is related to the light bulb activity.
This activity was included in the University of New England Julia Robinson Mathematics Festival.