Three’s A Crowd: An Exploration of Subprime Tribonacci Sequences

Abstract

A subprime Fibonacci sequence follows the Fibonacci recurrence, where the next term in a sequence is the sum of the two previous terms, except that composite sums are divided by their least prime factor. We extend the recurrence to three terms, investigating subprime tribonacci sequences. It appears that all such sequences eventually enter a repeating cycle. We compute cycles arising from more than one billion sequences, classifying them as trivial, tame, and wild. We further investigate questions of parity and primality in subprime tribonacci sequences. In particular, we show that any nonzero subprime tribonacci sequence eventually contains an odd term.