On Some Important Sequences and Their Relation with Pythagorean - Fermat Triples

This article introduces some important sequences and their connection with the hypotenuse of the Fermat family triangle with the NSW, Jha, and Pell sequences. Defining an exciting fact about the sequence, {3; 17; 99; 577; ...}, which consists of the first leg, has a corresponding second leg is an even perfect square such that the triple will be Pythagorean triple. Moreover, it shows the relation between Jha and NSW sequences.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.