The integer recurrence P(n)=a+P(n-phi(a)) I

2012/08/27 by Constantin M. Petridi, Petridi, Constantin M.
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Algorithms and Data Compression #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1208.5348

6 pages

openalex publication_date 2012/08/27 · arxiv created 2014/02/04 · arxiv updated 2014/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for a positive integer a the integer sequence P(n) satisfying for all n, -infty<n<infty, the recurrence P(n)=a+P(n-phi(a)), phi(a) the Euler function, generates in increasing order all integers P(n) coprime to a.The finite Fourier expansion of P(n) is given in terms of a, n, and the phi(a)-th roots of unity. Properties of the sequence are derived.

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