On Base 3/2 and its Sequences
Ben Chen, Richard Chen, Joshua Guo, Tanya Khovanova, Shane Lee, Neil, Malur, Nastia Polina, Poonam Sahoo, Anuj Sakarda, Nathan Sheffield, Armaan, Tipirneni
TL;DR
This paper explores properties and introduces new sequences related to integers expressed in base 3/2, including analogues of well-known sequences and their asymptotic behaviors.
Contribution
It presents novel sequences associated with base 3/2, extending classical sequences like Fibonacci and look-and-say to this non-standard base.
Findings
Sequences exhibit unique patterns in base 3/2.
Sorted Fibonacci sequences lead to Pinocchio sequences.
Reverse sorted Fibs lead to Oihcconip sequences.
Abstract
We discuss properties of integers in base 3/2. We also introduce many new sequences related to base 3/2. Some sequences discuss patterns related to integers in base 3/2. Other sequence are analogues of famous base-10 sequences: we discuss powers of 3 and 2, Look-and-say, and sorted and reverse sorted Fibonaccis. The eventual behavior of sorted and reverse sorted Fibs leads to special Pinocchio and Oihcconip sequences respectively.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Analytic Number Theory Research