A Note on Prime Fibonacci Sequences
Jeremy Alm, Taylor Herald

TL;DR
This paper introduces prime Fibonacci sequences, a new Fibonacci-like sequence variant where each term is the smallest odd prime divisor of the sum of the previous two, and proves their termination in powers of two.
Contribution
It defines prime Fibonacci sequences and proves their termination properties, extending the understanding of Fibonacci-like sequences with prime divisor conditions.
Findings
Sequences always terminate in a power of two
Sequences can be extended infinitely to the left
Provides mathematical proof of termination behavior
Abstract
In this paper, we define a variant of Fibonacci-like sequences that we call prime Fibonacci sequences, where one takes the sum of the previous two terms and returns the smallest odd prime divisor of that sum as the next term. We prove that these sequences always terminate in a power of two but can be extended infinitely to the left.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Analytic Number Theory Research · Advanced Mathematical Identities
