On Lucas Sequences of the First Kind With Finitely Many Primes

ISEF · 2022 Mathematics

Kim, Aaron · Bronx High School of Science

Overview

We strengthen a result of Jones by showing that for any integer P 1, the Lucas sequence {Un} defined by U0 = 0, U1 = 1, Un = P · Un1 + Un2 can be translated by a positive integer K(P) such that the shifted sequence with general term Un +K(P) contains no primes, nor terms one unit away from a prime.

Competition history

ISEF 2022 Mathematics · Entry MATH035 · Atlanta, Georgia, United States

Resources

ISEF abstract page

Related projects

ISEF · 2018

From Lucas Sequences to Lucas Groups

ISEF · 2025

On a Conjecture About a Recursive Prime Generating Sequence

ISEF · 2017

Independence of the Miller-Rabin and Lucas Probable Prime Tests

ISEF · 2019

Testing Chebyshev's Bias for Prime Numbers Up to 5*10^15

Closest projects by meaning, across every fair and year in the corpus.

Source: Regeneron International Science and Engineering Fair