Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers

2022/07/30 by Mustafa Ismail, Ismail, Mustafa, Ahmed Gaber +3
Arts and Humanities · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Experimental and Theoretical Physics Studies #FOS: Mathematics #Number Theory (math.NT) #Renaissance Literature and Culture

paper · pdf · doi:10.48550/arxiv.2208.00276

openalex publication_date 2022/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \lbrace P_k\rbrace_k≥0 be the Padovan sequence defined by P_k=P_k-2+P_k-3 with initial values are P₀=P₁=P₂=1. Let \lbrace R_k\rbrace_k≥0 be the Perrin sequence defined by R_k=R_k-2+R_k-3 with initial values are R₀=3, R₁=0, R₂=2. And let \lbrace J_n\rbrace_n≥0 be the Jacobsthal sequence defined by J_n=2J_n-1+J_n-2 with initials J₀=0, J₁=1. In this paper we determine all Padovan and Perrin numbers which are sum of two Jacobsthal number.

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