How to Create a New Integer Sequence
Tanya Khovanova
TL;DR
This paper reviews standard methods for creating new integer sequences, illustrating them with famous examples, and offers insights on what makes a sequence interesting to aid in sequence invention and analysis.
Contribution
It systematically discusses popular procedures for generating new sequences, providing definitions, examples, and insights to foster sequence creation and understanding.
Findings
Identified key procedures for creating sequences
Provided illustrative examples with famous sequences
Offered criteria for interesting sequences
Abstract
There are several standard procedures used to create new sequences from a given sequence or from a given pair of sequences. In this paper I discuss the most popular of these procedures. For each procedure, I give a definition and provide examples based on three famous sequences: the natural numbers, the prime numbers and the Fibonacci numbers. I also add my thoughts on what makes a sequence interesting. My goal is to help my readers invent new sequences, differentiate interesting sequences from boring ones, and better understand sequences they encounter.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Algorithms and Data Compression