Random Sequences from Primitive Pythagorean Triples

TL;DR

This paper analyzes the randomness properties of sequences derived from primitive Pythagorean triples, showing that certain classes exhibit different randomness characteristics depending on their ordering, with implications for sequence generation.

Contribution

It classifies PPT-derived sequences into groups and evaluates their autocorrelation and cross-correlation, revealing order-dependent differences in randomness.

Findings

Classes A and D differ in randomness when ordered by largest term.

Other orderings produce sequences with excellent randomness properties.

Sequences exhibit strong autocorrelation and cross-correlation characteristics.

Abstract

This paper shows that the six classes of PPTs can be put into two groups. Autocorrelation and cross-correlation functions of the six classes derived from the gaps between each class type have been computed. It is shown that Classes A and D (in which the largest term is divisible by 5) are different from the other four classes in their randomness properties if they are ordered by the largest term. In the other two orderings each of the six random Baudhayana sequences has excellent randomness properties.